Olds or or really old Books from Roulette game

[Asterix]

Hello to all players of the roulette game.
I once read in a subject, who spoke or who made all the joke about having Billedivoire's book "Jouer et Gagner" in French.
I'm not little or big crazy about spending €120 on a book.
But what do you actually know about old books on the game of roulette?
Did you know by chance that Blaise Pascal, the father of Baby Roulette, in 1659, had published a treatise on the game, and how mathematically it was possible to win against this game?
Yes this document a i have found it, but is in Latin language,normal this comming from year 1658.

I first warn the Administrators and moderators of this forum, that they have no fear, I would not post an entire book which is still currently for sale, because Amazon and the others, old books which was before in public edition, therefore Free, they as soon as they see one of his books which interests them, or which would be interesting for sale, they pay to the state a few Euros or Dollars, and after the book reappears in their stores for resale. (So here what counts is the date when I posted my thread, like that the bad bastards from Amazon won't be able to counter me, with the fact that I posted a book which is for resale with them, no because if they receive permission to republish after my publication date, they will not be able to do anything about this subject).

For his old books, which I was lucky enough to find, as soon as I find an ISBN for the book, I will attach it to you.
For free books, or free documents, here there is only one rule that counts, against plagiarism, and against the theft of ideas from elders author, having invented their game stratagems. As much systems as progressions. So I will need to send you the title of the book and its author.

[Asterix]

So i start from here with 10 pages from Blaise Pascal in latin language.

I give you original text in latin and translatet version from translator, so if exist latin word which translator don't have found translation, so you should be able to understand latin or better translated sentence.

Historia trochoidis, sive
cycloïdis, gallice : "la roulette" , in qua narratur quibus gradibus ad intimam
illius lineae [...]

iNter infinitas linearum curuarum species, si vnam circularem cxcipias, nulla est que nobis frequetius occurrat quam Trochoïdes ( Gallice ) la Roulette. Vt mirum sit quod illa priscorum faeculorum Geometras latuerit, apud quos de tali linea nihil prorsus reperiri certum est.

translated
Among the infinite species of curved lines, if you take one circular one, there is none that meets us more frequently than Trochoïdes (in French) la Roulette. It is surprising that it was hidden from the ancient Geometers, among whom it is certain that nothing of such a line is to be found.

Describitur à clauo Rotae: insublimi delato, dum Rota ipsa motu rotis peculiari, secundum orbitam suam reta fettur simul & circumuoluitur, initio motus sumpto, dum clauus orbitam tangit, vsq ; dum absoluta una conuersione, clauus idem iterum eandem taugat orbitam. Supponimus autem hic ad Geometriae speculationem, Rotam esse perfecte circularem ; clauum , punctum in circumferentia illius assumptum ; iter Rotae, perfecte planum ; orbitam denique perfecte rectam , quam circumferentia Rotae: continuo tangat; ambabus, orbita inquam & circumferentia, in uno eodemque plano inter mouendum ubique existentibus.

Hanclineam primus omnium aduettit Mersennus ex Minimorum ordine, circa annum 1615. dum rotarum motus attentius consideraret ; atque inde Rotulae: ei nomen indidit ; post ille naturameius & proprietates inspicere uoluit, sed irrito conatu.

Erat huic uiro ad excogitandas arduas eiusmodi quaestiones singulare quoddam acumen, & quo omnes in eo genere facile superatet: quanquam autein in iisdem dissoluendis, qua: praecipva huiusce negotij laus est, non eadem felicitate utebatur; tamen hoc nomine, de literis optime meritus est, quod permultis iisque pulcherrimis inuentis occasionem praebuerit, dum ad eorum inquisitionem eruditos de illis neq; cogitantes excitatet.

Ergo naturam Trochoidis omnibus quos huic operi credidit pares , inda gandam proposuit, inprimisque Galileo: at nemini res ex sententia cessit, omnesq ; de nodi Illius dissolutione des perarunt.

Sic Vinginti proxime abierunt anni ad usque 1634. quo Mersen-nus quum multas ac praeclaras proposiciones a Roberuallio regio

Translated Version:

It is described by the nail of the Wheel: carried to the sublime, while the Wheel itself, by the motion of the particular wheel, is drawn along its orbit and revolves at the same time, taking the initial motion, while the nail touches the orbit, etc.; while in absolute one turn, the same nail again navigates the same orbit. Now let us suppose here, for the sake of geometry, that the wheel is perfectly circular; a nail, a point taken in its circumference; the path of the Wheel, perfectly flat; in short, a perfectly straight orbit, which the circumference of the Wheel touches continuously; both, I say the orbit and the circumference, existing everywhere in one and the same plane between the motions.

Mersennus was the first of all to arrive at the Hancline from the order of the Minimus, about the year 1615, while he was considering more attentively the movement of the wheels; and from there he gave the name of Patulae; after that he wanted to look more naturally at the properties, but in vain.

This man had a singular acumen for devising difficult questions of this kind, and by which he easily surpasses all in that class: although he did not use it with the same success in breaking them down, which is the chief praise of this business; yet this name, of letters, he best merited, because he afforded the opportunity of finding many and the most beautiful of them, while for their inquiry he was learned about them; It will stimulate thinking.

Therefore the nature of Trochoidus was proposed to all those whom he believed to be equal to this work, and Galileo in particular; They passed away from the dissolution of his knot.

Thus, twenty years passed until 1634, when Mersen-nus received many and excellent propositions from the region of Roberuallio

So this are 1/10 pages
Blaise pascal, have used pseudonyme, so as Amos Dettonville as pen writer and others to others non mathematical idea.

[Asterix]

To word Mersennum = Marin Mersennum was an Abbe lived in the same era as Blaise pascal. See Law Mersenne. was a mathematician, physicist and in connection with Galileo which was same mathematician, geometer, physicist.... in this Era.

To hancline is other familly name.(More i don't have found)see genealogy or Ancestry in USA.

To roberualij in next page, here so as Pascal have many use pseudonym in his writing, here is possible Roberualij or Roberual was invented by Pascal. By Christiaan Huygens in 1663 in other latin write, the name comme appear as write in Pascal....

[Asterix]

second page:
first in Latin and second in English translation:

Matheseos professore solui quotidie videret, ab eodem suae quoque Trochoidis solutionem sperauit.

Nec vero eum sua spes frustrata est. Felici enim inquisitionis suae successu vsus Roberuallius, Trochoidis spatium spatij Rotae a qua describitur, triplum esse demonstrauit: ac tum primum huic figurae Trochoidis nomen e Graeco deductum imposuit, quod Gallico la Roulette, aptissime respondet. Mox ille Mersenno solutum a se problema, ac triplam illam rationem ostendit, accepta ab eo fide, id pertotum adhuc annum iri compressum, dum eandem rursus quaestionem omnibus Geometris proponeret.

Laetus hoc euentu Mersennus mittit rursus ad omnes Geometras: rogat vt de integro in eam inquisitionem incumbant; addit etiam solutum a Roberuallio problema: sed de modo nihil adhuc indicat.

Anno & amplius elapso, cum nullus propositae quaestioni satisfaceret ; Tertiam ad Geometras scribit Mersennus, ac tunc anno scilicet 1635. rationem Trochoïdis ad rotam vt3. ad i esse patefecit

Hoc nouo adiuti subsidio,problematis demonstrationem inuenerunt duo, inuentamque eodem ferme tempore ad Mersennum transmiserunt,altera Fcrmatius supremae Tholosane Curie Senator ; alteramCartesius nunc vitafunctus; vtramque,& alteram ab altera, & a Roberuallij item demonstratione diuersam: ita tamen,vt qui eas omnes videat , illico illius demonstrationem internoscat qui primus problema dissoluit. Ea enim singulari quodam caractere in-signitur , ac tam pulchra & simplici via ad veritatem ducit, vt hanc vnam naturalem ac rectam esse facile scias. Et certe eadem illa via Roberuallius ad operosiores multo circa idem argumentum di-mensiones peruenit, ad quas per alias methodos nemo forsan perueniat.

Ita resbreui percrebuit, neminique in tota Gallia Geometrie studiosiori ignotum fuit demonstrationem Trochoidis acceptam Roberuallio referendam. Huic autem ille duas sub idem ferme tempus adiunxit, vna est folidorum circabasim eius mensio: altera tangentium inuentio, cuius ipse methodum & inuenit & statim euulgauit, tam generalem illam ac late patentem, vt ad omnium curuarum tangentes pertinear. Motuum compositione methodus illa innititur.

Anno autem 1658. I. de Beaugrand cum illas de plano Trochoidis demonstrationes coIlegisset, quarum ad ipsum multa exemplaria peruenerant : itemque egregiam methodum Fermatij de maximis & minimis, vtrumq ; ad Galileum misit,tacitis authorum nominibu,

now the translation

Every day he saw Mathesus alone as a professor, from whom he also hoped to solve his Trochoid.

Nor indeed was his hope frustrated. For with the successful success of his investigation, Roberuallius demonstrated that the space of the Trochoid was three times the space of the Wheel by which it is described: and then for the first time he applied to this figure the name of the Trochoid, derived from the Greek, which corresponds most aptly to the French la Roulette. Soon he showed Mersenne the problem he had solved, and the threefold reason for it, accepted by him on faith, and it would be a further year before he would put forward the same problem again to all the geometers.

Mersennus, happy at this result, sends again to all the surveyors: he asks them to devote themselves entirely to the investigation; He also adds the problem solved by Roberuallius: but he does not yet indicate anything about the method.

A year and more passed away, when no one answered the proposed question; Mersennus writes the third to the Geometers, and then in the year 1635, the account of the Trochoides to the wheel vt3. He revealed that he was

Aided by this new aid, the two found a demonstration of the problem, and they transmitted the find to Mersenne at about the same time, the other Fcmratius supreme of the Tholosane Curia; the other, Descartes, now dead; both, and one from the other, and from Roberualli's demonstration also diverging: so, however, whoever sees them all, immediately internalizes the demonstration of him who was the first to dissolve the problem. For it is marked by a certain singular character, and leads to the truth in such a beautiful and simple way, that you may easily know that this one is natural and correct. And it is certainly the same way that Roberuallius arrived at much more laborious dimensions of the same argument, which perhaps no one could have arrived at by other methods.

Thus the resbreui grew, and no one in all Gaul was more ignorant of geometry than the demonstration of Trochoid received by Roberuallius. And to this he added two at about the same time, one is the measurement of leaves around its base; That method is based on a combination of movements.

And in the year 1658, when I. de Beaugrand had collected those demonstrations of the plane of the Trochoid, of which many copies had reached him: and likewise Fermat's excellent method of maxims and minimis, etc.; He sent to Galileo, without mentioning the names of the authors.

[Asterix]

Page 3 Latin

ac sibi quidem illa nominatim non adscripsit: iis tamen vsus est verbis,vt minus attente legentibus, quo minus se istorum profiteretur authorem ,sola demum impeditus modestia videretur. Itaque ad rem paululum interpolandam, mutatis nominibus,Trochoidem in Cycloïdem commutauit.

Non multo post Galileus, & ipse de Beaugrand vita cesserunt. Successit Galileo Toricellius,nactusque est inter illius manuscripta, quae omnia ad ipsum delata erant, ista de Trochoïde sub Cycloïdis nomine problemata ipsius de Beaugrand manu sic exarata quasi eorum author esset. Cognita ergo illius morte Toricellius,abolitam iam temporis spatio rei memoriam ratus, ea omnia secure iam ad se transferri posse arbitratus est.

Itaque anno 1644. librum edidit, in quo excitatam de Trochoïde quaestionem Galileo tibuit, quae: Mersenno debebatur: sibi primam eius dislolutionem arrogat, quam Roberuallij esse certum erat: in quo fane, vt candoris aliquid Toricellio defuit, sic & aliquid felicitatis. Neque enim sine quorumdam risu exceptus est in Gallia,qui anno 1644. hoc sibi asciuisset inuentum, cuius parens in viuis constanter iam per octo annos Roberuallius agnoscebatur ,qui quod suum erat non modo compluribus testibus adhuc viuentibus posset reuincere, sed etiam excusis Typo testimoniis, in quibus est quodda scriptum G.Desargues ann0 1640. Aug. mense Paris. editum; in quo nominatim habetur Trochoïdis problemata Roberuallij esse; methodum de maximis & minimis, Fermatij.

Ergo hanc iniuriam cum ipso Toricellio literis expostulauit Ro-beruallius; ac seuerius etiam Mersennus; qui tot ipsum argumentis, omnigenisq; testimoniis, etiam excusis, coarguit,vt veris victus Toricellius, hoc inuento cedere,illudq ; ad Roberuallium transscribere coactus sit: quod literis propria manu scriptis praestitit, quae etiamnum asseruantur.

Verum quia passim in manibus est Toricellij liber; contra, eius, vt ita loquar,recantatio paucis innotuit; Roberuallio tam parum de fama sua extendenda sollicito, vt nihil de ea recantatione emiserit in vulgus; multi inde in errorem, & ipsemet etiam inductus sum. Hinc factum est vt in prioribus scriptis ita sim de Trochoïde locutus, quasi eam princeps Toricellius inuenerit. Quo errore cognito, facien. dum duxi, vt quod iure Roberuallio debetur, hoc ipsi scripto restituerem.

Vsus hoc infortunio Toricellius, cum iam nec dimensionem spatij Cycloïdis , nec solidi circa basim primus inuenisse existimari posset

And translated version

and indeed he did not ascribe them to himself by name: yet he was opposed to those words, that is, to those who read them less attentively, the less he professed himself to be the author of them, in the end only his modesty seemed to hinder him. And so, to interpolate the matter a little, by changing the names, he changed Trochoid into Cycloïde.

Not long after, Galileo and de Beaugrand himself gave up their lives. He succeeded Galileo Toricelli, and among his manuscripts, all of which had been brought to him, these problems of Trochoïde, under the name of Cycloïdes, were drawn up by de Beaugrand's own hand, as if he had been the author of them. When Toricelli learned of his death, thinking that the memory of the matter had already been abolished by the passage of time, he thought that all these things could now be safely transferred to him.

And so, in 1644, he published a book in which he raised a question about Trochoïde to Galileo, which he owed to Mersenne: he arrogates to himself his first dissolution, which was certain to be Roberuallij's; For he was not without some laughter received in Gaul, who, in 1644, had learned of this discovery, whose parent had been constantly recognized among the living for eight years as Roberuallius, who was able to regain what was his not only by several witnesses still living, but also by excusing the testimony of Typus. in which there is something written by G. Desargues in 1640. Aug. in the month of Paris published; in which it is specifically held that the problems of Trochoides are Roberuallius; method of maxima and minima, Fermatij.

Therefore Ro-beruallius expostulated this wrong in letters with Toricelli himself; and Mersennus even more seriously; who, with so many arguments, of all kinds; by evidence, even with excuses, he forced Toricellius, who had been truly defeated, to surrender this and that; he was forced to transcribe at Roberuallius: because he presented the letters written with his own hand, which are still asserted.

It is true that Toricelli's book is scattered in the hands; on the contrary, his recantation, so to speak, was known to a few; Roberuallio was so little anxious to extend his fame, that he had not broadcast anything of that recantation to the common people; Many have been led astray by this, and I myself have also been led astray. Hence it came to pass that in my former writings I spoke thus of the Trochoïde, as if the prince Toricellius had found it. When they learn of this mistake, they will do it. while I thought that what was due by right to Roberuallius, I would restore this to him in writing.

This was a misfortune for Toricellius, since it could no longer be thought that he was the first to find the dimensions of the space of the cycloid, nor of the solid around the base.

Page 4 in latin :

abiis quibus perspecta rei veritas esset. Solidi circa axem Cycloïdis, mensionem aggressus est: ibivero non mediocrem difficultatem offendit: est enim illud altissimae cuiusdam & operosissimae inquisi-tionis problema; in quo cum veram assequi non posset,verae proxi. mam solutionem mifi; ac solidum illud ad suum Cylindrum esse dixit, sicut II. ad 18. ratus errorem illum a nemine reselli posse. verum nihilo fuit hoc etiam in loco felicior ; Nam Roberuallius qui veram ac Geometricam dimensionem inuenerat, non modo suum illi errorem, sed etiam veram problematis resolutionem indicauit.

Toricellius non multo post fato conceflit. At Roberuallius sola simplicis Trochoïdis eiusque solidorum dimensione non contentus, omnes omnino Trochoïdes siue protractas siue contractas inquisitione complexus est,easque excogitauit methodos, quae ad omnem Trochoïdis speciem pertinerent : eademque facilitate tangentes darent; plana , & planorum partes dimetirentur ; centra grauitatis planorum; ac postremo solida circa basim circa axem, patefacerent. Quamvis enim integras tantum Trochoïdes dimensus sit ; tamen ad Trochoïdum partes nihil mutata eius methodus non minus expedite adhiberi potest; vt qui illud Roberuallio inuentum abiudicet,merito cauillator habendus sit.

Nec vero ea omnia apud se celauit RoberualIius, sed scriptis mandata publice, priuatimque, atque etiam in celebri selectorum virorum Matheseos peritissimorum coetu , per complures dies legit, & cupientibus describenda permisit.

Eo perducta Roberuallij induftria Trochoïdis cognitione,ibi per 14.annos substiterat, cum me ad abdicata pridem Geometris studia repetenda improuisa occasio compulit. Tum vero eas mihi paraui methodosad dimenfionem , & centra grauitatis solidorum, planarum & curuarum superficierum , curuarum item linearum ,vt illas vix quicquam effugere posse videretur: atque adeo vt id in materia vel difficillima periclitarer, ad ea quae: de Trochoïde vestigandafupererant aggressus sum; nepe centra grauitatis solidorum Trochoïdis , & solidorum ex eius partibus exurgentium; dimensionem , & centra grauitatis superficierum omnium istorum solidorum; ac postremo dimenfionem, & centra grauitatis ipsiusmet lineae curuae CycIoïdis, eiusq; pattium.

Ac primum centra grauitatis solidorum semisolidorum indagaui, & opemeae methodi assecutus sum; quod mihi sic arduum est visum quasvisalias insistentibus vias,vt periculum facturus, an ita res esset quem admodum mihi persuaseram,hanc omnibus Geometris,

And translated :

and indeed he did not ascribe them to himself by name: yet he was opposed to those words, that is, to those who read them less attentively, the less he professed himself to be the author of them, in the end only his modesty seemed to hinder him. And so, to interpolate the matter a little, by changing the names, he changed Trochoid into Cycloïde.

Not long after, Galileo and de Beaugrand himself gave up their lives. He succeeded Galileo Toricelli, and among his manuscripts, all of which had been brought to him, these problems of Trochoïde, under the name of Cycloïdes, were drawn up by de Beaugrand's own hand, as if he had been the author of them. When Toricelli learned of his death, thinking that the memory of the matter had already been abolished by the passage of time, he thought that all these things could now be safely transferred to him.

And so, in 1644, he published a book in which he raised a question about Trochoïde to Galileo, which he owed to Mersenne: he arrogates to himself his first dissolution, which was certain to be Roberuallij's; For he was not without some laughter received in Gaul, who, in 1644, had learned of this discovery, whose parent had been constantly recognized among the living for eight years as Roberuallius, who was able to regain what was his not only by several witnesses still living, but also by excusing the testimony of Typus. in which there is something written by G. Desargues in 1640. Aug. in the month of Paris published; in which it is specifically held that the problems of Trochoides are Roberuallius; method of maxima and minima, Fermatij.

Therefore Ro-beruallius expostulated this wrong in letters with Toricelli himself; and Mersennus even more seriously; who, with so many arguments, of all kinds; by evidence, even with excuses, he forced Toricellius, who had been truly defeated, to surrender this and that; he was forced to transcribe at Roberuallius: because he presented the letters written with his own hand, which are still asserted.

It is true that Toricelli's book is scattered in the hands; on the contrary, his recantation, so to speak, was known to a few; Roberuallio was so little anxious to extend his fame, that he had not broadcast anything of that recantation to the common people; Many have been led astray by this, and I myself have also been led astray. Hence it came to pass that in my former writings I spoke thus of the Trochoïde, as if the prince Toricellius had found it. When they learn of this mistake, they will do it. while I thought that what was due by right to Roberuallius, I would restore this to him in writing.

This was a misfortune for Toricellius, since it could no longer be thought that he was the first to find the dimensions of the space of the cycloid, nor of the solid around the base.
the truth of the matter would be understood by those who He set about the measurement of the solids about the axis of the Cycloides: indeed, he encountered no moderate difficulty: for it is the problem of a very deep and laborious investigation; in which, when he could not attain the truth, he came close to the truth. I will give you my solution; and he said that it was solid to his cylinder, as II. at 18. thinking that this error could not be restored by anyone. but this was by no means more successful in this place; For Roberuallius, who had found the true and geometrical dimension, not only told him his error, but also the true resolution of the problem.

Toricellius conceived not long after his fate. But Roberuallius, not content with the simple Trochoides alone and the dimensions of their solids, investigated all the Trochoides altogether, whether extended or contracted, and devised methods which would pertain to every species of Trochoides: and would give tangents with the same facility; the plains and the parts of the plains should be released; centers of gravity of planes; and lastly the solids around the base around the axis, they would reveal. For although only whole Trochoides have been measured; yet his method can be used no less expediently for the parts of the Trochoides; for he who disobeys that found by Roberuallius, should be considered a custodian by merit.

Nor indeed did Roberualius conceal all these things from himself, but he read the written orders publicly, and privately, and even in a famous company of select men, the most skilled Mathesians, for several days, and allowed them to be copied by those who wished.

Brought there by Roberuallius to the knowledge of Trochoides, he had stayed there for 14 years, when an unpromising opportunity forced me to resume my studies of Geometry, which I had abandoned long ago. And then I prepared for myself methods for measuring them, and the centers of gravity of solid, flat, and curved surfaces, which were also curved, and it seemed that hardly anything could escape from them; perhaps the centers of gravity of the solids of the Trochoides, and of the solids rising from its parts; the dimensions and centers of gravity of the surfaces of all these solids; and lastly the dimensions, and the centers of gravity of the lines of the curua CycIoides, eiusq; pattium

And for the first time I traced the centers of gravity of solid semi-solids, and I obtained an opium method; because it seemed so difficult to me that any visible roads would be dangerous if they were to do so, which I had very much persuaded myself,

[Asterix]

5
etiam constituto praemio, inquisicionem proponere decreuerim.
Tunc scilicet latina illa scripta quaquauersum missa vulgaui ; ac dum illa de solidis problemata inuestigantur, reliqua ego omnia dissoIui, quemadmodum sub huius scriptionis finem exponam,vbi de Geometrarum responsis prius dixero.
Illa vero responsa duplicis sunt generis; quippe diuersi sunt scribentium genij Quidam soluta a seproblemata , atque ita itis sibi in praemium esse contendunt. Horum scripta legitimo examine propediem excutientur. AIij ad problematum quidem solutionem non aspirant, sed su as tantum in Cycloïdem commentationes exponunt.
Horum in literis multa praeclara, & eximiae dimetiendi Cycloïdis plani rationes habentur ; imprimisq; in epistolis Fluxij Leodiensis Ecclesia: Canonici, Richij Romani, Eugenij Bataui qui primus om¬nium detexit eam plani Trochoïdis portionem trilineam , quae his tribus lineis comprehenditur, scilicet quarta parte axis ad verticem terminata, recta ad axem ab initio illius quartae partis perpendiculariter ordinata vsque ad Trochoïdem , & portione curuae Trochoïdis inter duas praedidas redas terminata, spatio rectilineo dato aequalem esse , atq; adeo illi aquale quadratum absolute exhiberi: quod idem in Epistola VVren Angli eodem fere tempore scripta reperi.
Cycloïdis etiam,eiusque partium, itemque solidorum circabasim tantum dimensionem accepimus ab Allouero e focietate Iesu Tholosano; quam, quia ille typis editam misit, attentius inspiciens, non sine admiratione cognoui cuncta illa quae: ibi habentur problemata, etsi non alia sint quam quae iam pridem a Roberuallio soluta sunt, ta¬men ab illo nulla prorsus Roberuallij facta mentione, quasi a se pri¬mum soluta, proferri. Quanquamenim diuersam fecutus est metho¬dum, neminem tamen fugit quam promptum ac procliue sit iam inuentas propositiones noua specie habituq; producere: tum excognita illarum solutione, nouas soluendivias comminisci.
Egi igitur sedulo cum Carcauio, tum vt Allouerum moneret, quod pro suo venditabat, Roberuallij esse, vel nullo negotio excius inuentis elici ; tum etiam vt viam ipsi explanaret qua eo Roberualiius peruenerat; nam haec inter honestos viros citra periculum communicantur. Me igitur anmtente scriptum est ad Allouerum, il¬lam quae Roberuallium eo perduxerat methodum, cuiusdam figurae quadratura niti, ab eodem pridem inuenta, quam figuram delineat circini ductus in recti Cylindri superficie, quaesuperficies in planum porrecta, mediam cuiusdam lineae efficit partem , quam Roberualius

Here page 6

Trochoïdis Sociam siue Gemellam dixit, ex qua quae ad axem rectae ad angulos rectos ducuntur, aequales sunt ductis exTrochoïde, demptis illis quae ex Rota ducuntur. In hoc vero nonmediocrem me ab Allouero gratiam iniisse credidi; quandoquidem ipse in suis literis quae adhuc habentur, de istius figurae quam Cycloï-Cylindri-cam appellat, quadratura ita loquitur, quafi que à sua notitia longe absit & quam nosse vehementer expetat.
Haecpro Carcauio,cui tam multa scribere non vacabat,quidam ip-sius amicus ad Allouerum seripsit, cui vicisim rescripsit Allouerus.
Sed inter missa a Geometris scripta, nullum ipsius VVren scripto prestantius. Nam praeter egregiam dimetiendi Cycloïdis plani rationem, etiam curuae & eius partium cum recta comparationem aggreffus est. Propositio eius est,Trochoïdem ad suum axem esse qua-druplam; huius ille enuntiationem sine demonstratione misit; & quia primus protulit, inuentoris laudem promeritus est.
Nihil tamen de illius honore detractum iri puto , si quod verissimum est dixero,quosdam e Gallia Geometras ad quos illa enunciatio perlata est, & in iis Fermatium, eius non difficulter demonstrationem inuenisse. Dicam insuper Roberuallium nihil sibi nouum af¬ferri plane ostendisse; statim ac enim de ea propositione audiit, inte¬gram eius demonstrationem continuo subiecit, cum pulcherrima methodo ad omniem linearum curuarum dimensionem, quam me¬thodum ipse dum alia inde grauiora consectaria sperat eruere, diu occultam habuerat. Et certe eadem ille methodo vsus erat ad com¬parandas Spirales lineas cum Parabolicis, qua de re in operibus Mersenni nonnulla reperias.
Haec Methodus compositione item motuu innititur, vt & illa tagentium. Nam sicuti motus compositi directio tangentem dat, sic eius celeritascurue longitudine essicit; quod fane nunc primum reseratur Haec sunt quae in eorum qui praemium non respiciunt scri¬ptis ammaduersione dignissima reperi; de caeteris,peracta demum discussione, dicemus; quam quidem prima O ctobris die aperiri constitutum erat, sedad reditum vfque Carcauij, qui jamjam affuturus nuntiatur, rejicere necesse fuit. Tum vero iudicabitur an aliqui quatuor illis legibus satisfecerint, quas nos editis Mense lunio scriptis promulgauimus.
1.    Vt solutio Carcauio denuntiata & apud eundem rescriptasit in¬tra praestitutum tempus,nimirum primum Octob. diem; qui intrat, (haec  nostra verba) praestitutum tempus D de Carcauy signisicauerit.

2.   Vt illa denuntiacio instrumento publico fiat, ad tollendam frau¬dis suspicionem.

Here i start translation from this 2 pages.

5
even after the reward had been established, I resolved to propose an inquiry.
Then, of course, the written Latin was sent everywhere to the vulgar; and while those solid problems are being investigated, I have broken up all the rest, as I will explain at the end of this writing, where I will first speak about the answers of the Geometers.
But those answers are of two kinds; for there are divers writing geniuses. The writings of these will soon be shaken by a legitimate examination. Indeed, they do not aspire to the solution of the problems, but only comment on the Cycloides.
In the letters of these, there are many excellent and exceptional reasons for the reduction of the plane of the Cycloides; especially in the epistles of the Church of Leodia: Canonici, Richius Romani, Eugenius Bataui, who first of all discovered that trilinear portion of the plane of the Trochoides, which is comprised by these three lines, that is, the fourth part of the axis terminated at the top, the straight line arranged perpendicularly to the axis from the beginning of that fourth part until to the Trochoide, and bounded by the portion of the Trochoide's bow between the two given reins, to be equal to the given rectilinear space, and so much so that the square water was presented absolutely to him: which I find the same in the Epistle of VVren of England written about the same time.
We have received only the dimensions of the cycloids, and of their parts, and also of the solids around the base, from Allouerus, from the study of Jesus of Tholos; which, because he had sent the printed edition, upon closer inspection, I learned, not without astonishment, all that: there are problems there, even if they are no other than those which had already been solved a long time ago by Roberuallius, yet by him there was absolutely no mention of Roberuallij, as if by himself first released, brought forward Although various methods have been used, yet no one escapes how quickly and easily the propositions already found have been adapted to a new form; to produce: then, having discovered the solution of those, new solutions were proposed.
I therefore acted diligently with Carcauius, and then he advised Allouer, that he was selling for his own, that Roberuallij was, or had no business, to find the elixir. then also that he should explain to himself the way by which Roberualius had arrived there; for these dangers are shared among honest men on this side. It was therefore written in my memory to Allouerus, that method which had led him to Roberualius, based on the quadrature of a certain figure.

And page 6.

He called the Trochoide the Consort or Twin, from which those which are drawn to the right axis at right angles are equal to those drawn from the Trochoide, minus those which are drawn from the Wheel. In this, indeed, I believed that I had received no mean favor from Allouerus; since in his letters, which are still preserved, he speaks of the quadrature of that figure which he calls Cycloï-Cylindri-cam, which is far from his knowledge, and which he vehemently desires to know.
For this reason Carcauius, to whom he had no time to write so much, a certain friend of his, sneaked to Allouerus, to whom Allouerus wrote in turn.
But among the masses written by the Geometers, none of the writings of VVren excels. For in addition to the excellent method of dividing the plane of the Cycloides, he also grasped the curua and its parts with a correct comparison. His proposition is, that the Trochoide is quadruple to its axis; of this he sent the statement without demonstration; and because he was the first to bring it forth, he earned the praise of the inventor.
However, I think nothing will be taken away from his honor, if I say what is most true, that certain geometers from Gaul to whom that statement was conveyed, and among them Fermatius, found a demonstration of it without difficulty. I will say, moreover, that Roberualius clearly showed that nothing new had been brought to him; for as soon as he heard of that proposition, he immediately submitted to its complete demonstration, with a most beautiful method for all the dimensions of the lines of the curias, which method he himself had kept hidden for a long time, while he hoped to derive from it other greater consequences. And certainly he used the same method to compare spiral lines with parabolic lines, which you can find some information about in the works of Mersenne.
This method is also based on the composition of movement, viz. For just as the direction of a compound motion gives a tangent, so its speed dries up in length; which is now being unlocked for the first time. of the rest, after the discussion is finished, we will say; which, indeed, it had been decided to open on the first day of October, but it was necessary to reject the return of the vf Carcauij, who was already announced to be there. And then it will be judged whether some have satisfied those four laws, which we promulgated by writings published in the last month.
1. As the solution announced at Carcauio and rewritten with the same within the appointed time, presumably the first of Octob. day; he who enters, (these words of ours) signified the appointed time of D de Carcauy.

2. That this announcement should be made in a public instrument, in order to remove the suspicion of fraud.

[Asterix]

Well, hello, so here I just came across an old character, and as the letter is written in Latin, unfortunately I don't know how to identify the character, all I know is cursive Roman writing. the writing style has the famous "s long or elongated", so if someone could help me identify this character, thank you, I am attaching a screen print close-up on the "s" and on the character or the Latin word, which I cannot identify.

So the latin word finish with "..atuendum" 1
so "S" Elongated is used as word "miserit" underscore in white.

[Asterix]

ok, i have decypher word.
Here the two last page, yes on start, it was write 10 pages, but is only 8 pages total.
So here the last latin version.

3.Vt demonstratio compendiaria, vel saltem certi cuiusdam casus calculus offeratur ; ex quo incelligi possit an qui eum mittit iam tum veram problematis solutionem tenere credendus sit. Aut certe ad consfirmandam assertionis veritatem , casus quem mox designabimus calculum miserit. At misso calculo solo, tunc de vero aut falfo omnino statuendum veniet, provt calculus velverus vel falsus iudicatus fuerit.



4. Vt deinde per otium , omnium propositorum casuum demonstratio mittatur, caque vera & omnibus partibus Geometrica abijsiudicetur, quos Carcauius arbitros asciuerit. Si quis tamen error calculi in integras illas omnium casuum demonstrationes irrepserit, eum putauimus condonandum : quia calculi necessitas cessat, vbi adest demonstratio: adeoque tunc semper ignoscendus est: error in calculo interueniens.

Si duo his conditionibus satisfecerint, primus primum praemium, secundus secundum accipiet ; si vnus modo. solus vtrumque obtinebit. At qui vel vni illarum legum defuerit, excidet ille quidem praemio, non item honore , quem pro scriptorum quae ille publicare poterit praetio, meritum consequetur; non enim vllas dispensando honori leges apposui ,qui prorsus mei iuris non erat; sed tantum praemijs, quorum mihi plena & soluta potestasfuit.

Quod si, re legitime discussa, nullus problemata dissoluisse reperiatur, tunc meas ipse solutiones proferam ,vti me in scriptis meis, postquam praestituta ad id prima Octobris dies aduenisset, facturum esse pollicitus sum. Itaque calculum meum iam euulgare coepi, multisque ilium fide dignissimis personis tradidi manuscriptum : & inter alios Carcauio, Roberuallio, D. Galois Regio Tabellioni Parisijs degenti,ac compluribus alijs Galliae viris dignitate & eruditione praestantibus, qui die accepti a me calculi diligenter annotarunt.

Hunc vero propterea statim edendum non censui, vt si qui inipsa discussione eum inuenisse reperti sint, id ab ipsis ante vulgatam solutionem meam factum praedicem: sin minus a nemine inuenta publicabo.

Quin etiam, quo tota Trochoidis natura pernoscatur ,fequentia adiungam problemata, quorum nonnulla mihi videntur non minus ad soluendum difficilia , quam quae huc vsque proposita sunt.

1. Puncto Z dato quocumque in Trochoide simplici, inuenire

centrum grauitatis curuae Z A inter assignatum punctum Z & verticem A interceptae.

2.  Inuenire dimensionem superficiei curuae ab  eadem curua Z A

descriptae,dum ipsa Z A circumuoluitur ,vel circabasim, qui casus facilis est, vel circa axem: & siue conuersio proponatur integra, siue dimidiata ,veleius quaecumque pars.

3. Omnium praedictarum superficierum a curua Z A descriptarum tam partium, quam integrarum,centra grauitatis assignare.

Et hoc quidem tertium omnium inuentu difficillimum mihi extitit. Esto ergo idem solum ac vnicum prae caeteris ad discutiendum propositum.

Inomnibus autem illis problematibus supponitur circuli quadratura , vbicumquc supponendafuit.

Haec sunt quae de natura Trochoidis retegenda restabant, quorum solutionem ad vltimum vsque Decembris diem huius anni 1658. comprirmemus, vt si quis ea intra id tempus inuenerit, inuentionis gloria potiatur. At hoc elapso, si nemo attulerit, ipsimet afferemus: atque ipsam etiam generalem dimensionem omnium linearum curuarum cujusuis Trochoidis vel prottactae vel conttracte ; quae non rectis lineis, sed Ellipsibus aequales ostendentur.

Hic nostrae in huius lineae natura rimanda peruestigationis limes fuit j quare vt totam hanc narrationem in summam contraham.

Primus Marsennus ,hanc lineam in natura rerum aduertit,nec tamen eius naturam peruidere valuit.

Primus Roberuallius, & naturam retexit, & tangentes assignauit, ac plana & solida dimensus est; & centra grauitatis, tum plani, tum plani partium,inuenit.

Primus VV ren, lineam curuam dimensus est.

Ego denique primus, solidorum, ac semisolidorum Trochoidis & eius partium, tum circa basim, tum circa axem, centra grauitatis inueni. Primus ipsiusmet lineae centrum grauitatis. primus dimensionem superficierum curuarum praedicta solida, semisolida, eorumq; partes comprehendentium. Primus centra grauitatis talium superficierum integrarum & diminutarum. Ac primus dimensionem omnium linearum curuarum cujusuis Trochoidis, tam protactae, quam conttactae.      

Decim. octob. 1658.

And now translated version.

3. As a summary demonstration, or at least a certain calculus of a certain case is offered; from which it can be understood whether he who sends him is to be believed to hold the true solution of the problem. Or at least to confirm the truth of the assertion, he sent the calculus which we shall soon describe. But when the calculus alone is sent, it will then come to be decided entirely whether it is true or false, after the calculus has been judged to be true or false.



4. Then, at leisure, a demonstration of all the proposed cases should be sent, and the truths and all the geometrical parts should be adjudged, which Carcauius had arbitrarily assigned. If, however, an error of calculation crept into those complete demonstrations of all cases, we thought he should be pardoned: because the necessity of calculation ceases, where the demonstration is present: and so then it is always to be forgiven: an error entering into the calculation.

If two have satisfied these conditions, the first will receive the first prize, the second the second; if one way he alone will obtain both. But he who has failed in even one of those laws, will indeed be cut off by the reward, not also by the honor, which the merit will obtain for the value of the writings which he can publish; for I did not, by dispensation, apply laws to honor, which was not entirely my right; but only the rewards of which I had full and free power.

And if, after the matter has been legitimately discussed, it is found that none of the problems have been resolved, then I will bring forward my own solutions, as I promised to do in my writings, after the first day of October had arrived. And so I began to publicize my calculus, and I delivered the manuscript to many persons worthy of his trust: and among others, D. Galois, who lived in the region of Tabellion Parisij, at Carcauio, Roberuallio, and to several other men of Gaul of distinction and erudition, who carefully annotated the calculus on the day it was received from me.

For this reason, however, I did not decide to publish it at once, for if it is found that those who have discovered it through indecent discussion, I will announce my solution, which was previously published by them;

Moreover, when the whole nature of the Trochoid is known, I will add frequent problems, some of which seem to me no less difficult to solve than those which have been proposed up to now.

1. Find the point Z given anywhere on the simple trochoid

the center of gravity of the curve Z A between the assigned point Z and the vertex A intercepted.

2. Find the surface area of the curve from the same curve Z A

described, while Z A itself is revolved around, either around the base, which is the easy case, or around the axis;

3. To assign the centers of gravity of both parts and wholes of all the aforesaid surfaces described by the curve Z A.

And indeed this third finding of all was the most difficult for me. Be the same, then, as the sole and the only one before the rest to discuss the purpose.

But in all these problems the squaring of the circle is supposed, wherever it was supposed.

These are the things that remained to be discovered about the nature of the Trochoid, the solution of which we will confine to the last day of December of this year 1658, so that if anyone finds them within that time, the glory of the discovery may be obtained. But when this has passed, if no one has brought it, we will bring it ourselves: and also the general dimension of all the lines of the horns of each Trochoid, either extended or contracted; which will not be shown in straight lines, but in equal ellipses.

Here was the limit of our investigation into the nature of this line, and therefore I will summarize this whole narrative.

Marsennus was the first to point out this line in the nature of things, and yet he was not able to perceive its nature.

The first Roberuallius, and discovered nature, and assigned tangents, and measured planes and solids; and he found the centers of gravity, both of the plane and of the plane of the parts.

The first VV ren, measured the gray line.

Finally, I was the first to find the centers of gravity of the solid and semi-solid Trochoid and its parts, both around the base and around the axis. The first line is the center of gravity. the first is the dimension of the surfaces of the aforesaid solid, semi-solid, etc.; the parts that comprise The first centers of gravity of such surfaces are intact & reduced. And he was the first to determine the dimensions of all the lines of the horns of each Trochoid, both extended and contacted.

The tenth October 1658

[Asterix]

Hello, but now that is enough for me the Latin language.
So now I'm passing on a book where I don't have the right to publish it entirely, since it was taken out of the archives and taken over by a brand for resale.... either because they saw it, or because people was interested in reading this book, so they just want to resell even if their own mother, could bring them money, they would put it up for sale.
Okay, enough talking:

Pascal, inventor of roulette, said: "I will provide the means to destroy this game".

And, a century ago, Napoleon: "Calculation will conquer the game".

Prophecies made today by the New Scientific Theory
OF the game of Roulette, Trente et Quarante, etc.

giving the two laws which govern them and with the help of which we obtain blows on the Bank without progressions
BY
Théo d'ALOST
�

[Asterix]

here with century ago, because book, was publish in year 1910.

[Asterix]

So this book will speak:

1° Hits on the bank with equal mass = no progression;

2° Persistent or indefinite ecarts don't possible;

3° Narrowing of the "point of ecarts" at will, in a word complete victory on roulette and everything that we qualify as "game of hazard".

And i start here now, nothing after, with value, wo you should know as player:
Series of 1 in spin = on 1000 spins coming = 500 here nothing 0 outcoming integrated.
Series from 2 and more in spin = 500 without count 0....
And here you divide more time 50% to all two chance, so as Red and Black. or Even and Odds. or 1-18 and 19-36. So to 1000 spin = 250 Red and 250 Black one 1 series and 250 2 and more series.

So yes any new time, in one day, on 250 spin/days, so as make series 200 Red or 200 Black, don't be possible don't before Billions (number contain 15x 0 back on number)years.
Outcoming from series 25 = 1 time each 100 year, and i have follow so series on Red color. in my old Casino. It gave player, wo run to coming on table by 14th spin, played to break, with paroli but was all dead in money, after 21th spin.

And each played Day, a from series 1-10 are possible to come out. So same, each day, a player wo play paroli to break a chance to follow, each day so, this player have possibility to sunk in deepness of payment.So Series of 9 or 10 have possibility to start on first minute as the roulette table is open, or coming to start only 6-8 hours after opening roulette table.

 

[Asterix]

But, i should to open it, with this self warning message from Author.wo i self subscribe fully.
yes sure, this was in year 1910, but forgot, today it give this false casino.

In this regard, I cannot stress enough that it is dangerous to frequent these clandestine houses, a thousand unpleasant surprises await the player there. There is only one house in the world where gambling is practiced in a correct, fair manner, and that is at the Monte-Carlo Casino.

Everyone who has visited a casino has been able to make this remark (we have heard it made a hundred times): "Is it possible to play so stupidly? It's silly! » And it is very true; We sometimes see players maneuvering in such a clumsy way that anyone who knows the game is immediately struck by it.

Playing red and black simultaneously, out of three dozen, sow on the table a number of coins such that the luckiest hit of one of all the bets would not cover the expense made. This fact observed, we can logically deduce that:

If we can play stupidly, we can play less stupidly, then better, well, absolutely well and surely win.

This winning clientele, of which we speak above, and which we refer to somewhat disdainfully as "people who make a living from gambling", forms a very large contingent of this very special world of players. They are, in any case, researchers. They manage, through patience, to find, without really knowing why, a somewhat slow game which gives little difference and which, in practice, leaves them, at a given moment, with a few winning moves. . They are content with it, and get married. They know, from experience, that if they continued, these units would return to the bank. Hence again this cliché: "You have to know how to be satisfied with a little", and this little, even if it is only two or three units, is enormous, because these units can be 5, 10, 20 and up to 6,000 francs.

Today money are €, so you should change value to maximum autorised to play on table.

We personally knew a household; the woman alone played. She sat down at noon, and at the stroke of 4 she got up, her work was finished. She always played the same game with the unit of 5 francs and it was only after five years that they retired having realized the fortune they had decided to conquer. He is the finest example of wisdom and perseverance that we have ever had the pleasure of encountering.

It is also proof, alongside a hundred others, that the Monte-Carlo administration leaves the players who win perfectly alone, and only evicts from its salons the incorrect or dishonest players who then pose as victims and insinuate , even affirm, that the reason for their ostracism is the fear that the bank would have had of their game.

here i have perfect vision, in era 1910, yes, this can are correct, but today, if a casino see it a winner wo win too many money, no no, she have make experience with Bonaparte, Garcia and Wells, so no, it don't would have a new scorer, wo want explode too many her bank reserve. So it accept it Winner, but it give limit to win...

[Asterix]

So here now, i hold with quote, because is a book we are sale by brand.
But It don't be prohibited from simply discussing its content with you.

So in the book it is written a proof of the role of zero in the cylinder. Yes, here when Blaise Pascal created roulette, he organized everything so that all the chances of the game were integrated. And of course he didn't integrate them simply by throwing the odds inside the cylinder. No here in addition he carefully placed the 0 in the cylinder, no such putting in the center of the number between the 28 and the 12; starting from the center of zero since if we draw a straight line ending at its end between the 30 and the 11, thus we could see that on one side there will be an imbalance between the Even and the Odds. But Pascal wanted to have a perfect balance of chances, which is why the zero is found between the 26 and the 32 and dividing the 5 and the number 10.
Thus we find, 9 Red, 9 black, 9 odd and 9 even and 9 1-18 and 9 19-36, and on the other side we will also find the identical numbers of chances Red, black, odd, even 1 -18 and 19-36.

[Asterix]

The author Théo d'Alost, go even further or more in depth. By listing: Since there is this real balance between the chances in the game. We must exclude any idea of chance, if we admitted this false definition, all the spins would be new. And they could make this balance has never been achieved, but we all know that it is totally impossible.

And in chapter II, he proves the absurdity of systems, reviewing "here he uses the word figure, and he uses the word form, while I will instead use the term currently using either Possibility.

Well, so we start with the Fig. of 1 or 1spin from the beginning, here we are in complete agreement, we don't know anything else yet, either this will be example Red or Black. So 2 possibilities

TO First to 4th. spin with his possibilities

see here:


To first yes, here it give just Red or Black (2 possibilities)
To second; here RR or RB or if first was black BB or BR (4 possibilities)
To Third; here it give each more is 2 time more more possibilities (8 possibilities)
and with 4 spin = (16 possibilities)
with 5 = (32 possibilities).....

But so, each time, if we wait on first spin, so each time we can delete 50% of possibilities.
 

[Asterix]

So here now next step, each figure should be numbered,and yes the figure starting with Black color as first spin, use same code number as this with Red Color.

Does this now give you a better understanding of what this is going to mean?
No?
If I note for example the outputs, and at each spin, I add the appropriate code to the figure, which this has just given, such as the code 1 = series. So on 8 spins one after the other it will be 1-1-1-1-1-1-1-1, But if such on the 3rd spin, here there is a break so color change is 1 -1- here you will need to enter the code 2 which gives 1-1-2.
Either for the next spin it will either return to Red or it will stay on black. If for the 4th spin, it returns to Red, it will be 1-1-2-3 and if it continues to the black side = 1-1-2-4.

And now I ask you the following question, which will give you light. If the figure 1-1-2-3 had come out 4 spins before, and the player just wants 4 spins of play, then what chance does this figure now come back after 1-1-2-3 a new figure 1 -1-2-3?
50% since the other solution would have been 1-1-2-4.
Here I'm talking about playing figures, not spins.
But a classic series as we know.
Spin 1 = 50% Either as an example R
2 spins of a series in Red or Black. = 50% = 1/2 R
3 spin of a series in red..."""" =50% of 50% = 1/4 R
4 spins in a series in red.."" =1/8, but each time = 50% following, spins from before.

And here too, during the numbering, the player must carefully prepare his figures containing the numberings, otherwise he himself will quickly get involved with the brushes, being obliged to carefully re-check each figure. So for the codes, as it will work according to the figures, whether Red or Black, the numbering will not change between the two colors, since once again, it is the figure which is registered, not the spin number.