Elements of philosophy, the first section, concerning body / Written in Latine by Thomas Hobbes of Malmesbury. And now translated into English. To which are added six lessons to the Professors of Mathematicks of the institution of Sr. Henry Savile, in the University of Oxford. [J. Wallis and S. Ward].

  • Hobbes, Thomas, 1588-1679.
Date:
1656
Catalogue details

Licence: Public Domain Mark

Credit: Elements of philosophy, the first section, concerning body / Written in Latine by Thomas Hobbes of Malmesbury. And now translated into English. To which are added six lessons to the Professors of Mathematicks of the institution of Sr. Henry Savile, in the University of Oxford. [J. Wallis and S. Ward]. Source: Wellcome Collection.

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    ■ To the third Article together with its Table, you fay ,itfallsinthcruincofthcfecond> and that the fame is to be underftood of the fixtb, jcvcntb, eighth and nineth. For confutation whereof I need to fay no mere, bat that they all Hand good by the confutation of your objecti¬ ons to the lecond. .... * To the fourth Article'you Cty',ihe defeription 'of thofefiurvilineall Figures is cafie. True, to fome mcn 3: and now that I have (hewed you the way, ’tis eafie enough for you alfo. For the way you propound is wholly tranferibed out of the Figure of the vecond Article, which Ar¬ ticle you had before rejected. For feeing the Lines H F, G E, A B, &c. are equall to the Lines C Q_2 CO, CD; and the Lines QF, O E, D B, equall to the Lines C H, C G, CA; the Proportion of DB to O E, will be triple (/that is, triplicate) to the Proportion of . CO toGEj* and the Proportion of D B to Q_F, triple to the Proportion ol C D to C Qj gnd consequently, becaufe the Complement B D C F E B i$ made by the decreafe of A C in triple Proportion to that cf the decreafe of C D, it will be (by the fecond Article) a third part of the Figure A B E F C A. So that it comes all to one pafs, whether we take triple Proporti¬ on in decreafing to make the Complement, or triple Proportion in increafing to make the Fi- gurejfor the Proportion of hi F to B A,is triple to the Proportion of C LI to C A.VVherefore you have done no more but what you have feenfirft done, faying that from your conftrudion you prove not the Figure to be triple to the Complement5 perhaps becaufe you have proved the con- • '__ T*)£vi tt-nmtYdt Rnf imnr'ttfiiv AifErc rrnm rnink. in rnaf tfon 'rail ill proved, becaufe I call the Proportion of one to two triple, or triplicate of that of one to cLht 5 which you fay is falfe, and hath infeded the fourth, fifth, mneth, tenth, eleventh, thir¬ teenth, fourteenth, fifteenth, fixteenth,feventeenth and nineteenth Articles qf the lixteentteChap- ter. But I fay, and you know now, that it is true 5 and that all thefe Articles, are Demon- . fixated. . • tr Laftlyyou add, Tuvero, in prefer, te Articulo,&c. idcjt,ycu bid find m many mean Pro- . portionals M one will, between two given Lines3 a/s if that could not be done by the Geome¬ try of Plains, You might have left out Tu vero to Seek an Ego qitidem. But tell me, do you think you can find two mean Proportionals (which is lefs then as many as one will ) by the Geometry of Plaines ? YVe fhall lee anon how you go about it. I never fai,d it was im- poftible, and if you look upon the places cited by you inore attentively, you will find your felt. >• miftaken But I fav, the way todo it has not b^nyct fuund out, and therefore it may prove y a folid Probleme for any thing yo« Enow. ■ ; ■ )..r -To V? The fifth Article you reject, becaufe it citeth the Corollarie of the twenty-eighth Article of the thirteenth Chapter, where there is never a word to that purpofe. But there is. in the twenr ty-fixth Article 3 which was my own fault, though you knew not but it might have been the P^0 the tenth you object for aim oft three leaves together? againft thefe words.of mine, Becaufe the fixth Figure) B F is to B E in triplicate Proportion of C V to F E, therefore iny/cr- tine:, F E is to^CV in triplicate. Proportion of B F to B C. This you objected then,,. . But now that I have taught you fo much Geometry, as to know that of three Qiianti tie's,. begin- in? at the leaf, if the third be to tbefirfl in triplicate Proportion of the fc con d.toftbefir< alfo by conversion the firji to the fecond fail be in t; i plicate Proportion of the firJl to tfie'tlfirJ j. if it were to do again, you would not objtd it, , Jiriv Mv eleventh Article you would allow for demonftrated, if my fecond had been De;>onftrc- ted, upon which it dependeth. Therefore feeing your objedions to that Article are fuffickijtly anwered, this Article alfo is to be allowed. . viiLjaiiai The twelfth alio is allowed upon the 'fame reafon. What falfities you fhall finde inftichfbl- lowingPropofitions as depend upon the fame fecond 'Article* we fhall then fee when Iconic to the plach where you objed againft than. • “ ' _ * : To < <