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# Title: [Christiani Hugenii Zulichemii, Const. F. Horologium Oscillatorium. Sive De Motu Pendulorum Ad Horologia Aptato Demonstrationes Geometricae] Christiani Hvgenii Zvlichemii, Const. F. Horologivm Oscillatorivm. Sive De Motv Pendvlorvm Ad Horologia Aptato Demonstrationes Geometricæ (shelfmarks Leibn. Marg. 70; ZEN Leibn. Marg. 70)
# Folio 62, page id 799199311:0078
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CHLIOLTANLIINOEMIL
euurarum aquales duabus iltis, _HICCE D K C X C H, sive his aequalirectae
EVOLUTTONE. D C. Duabus auremCs DC, CHminor est recta D H. Frgohac
minor utique erit rect a D C. Scd DEmajor est quam D C, quia in
criansus CE angulus cestiectus. ErgoD u multominor quam
D F. Sicu et ergo punctum , hoc est extremitas AliC H, intra
ansulum D C E. Vnde apparet neque inter a e c ulquam illam
pertingere ad rectam CF. FrgO C E cangir curram a C in C; ac
proinde DC, cui c F ducta estperpendicularis, occurrit currx ad
angulos rectos. Quod crac demonstrandum.
Irinc etiam manifestum est curram A E C in partemunam in-
Dexam esse, e in eandem partem caram ac ipla a CB, cujus evo.
lutione delcripra est. Omnes enim cansentes lincae AHT C, cadun
exera sparium D C AH C: omnes vero rangenres linex a CD, in-
era dictum spatium. unde liquer caritatem a H C respicere con-
vexitatem ACD.
62
UErARUM
PROTOSITIOI
Mnis curva linea terminata, in unam partem cava. ut
ABD. potest in i pates dividi, ut si sinculis partibus
subtensa recta ua diit A B, BC, CD; Cd a sinculis
item divisionis punctis, ip saque curva extremitate recta du-
cantur curvam tancentes, ut AH, BO, CP, quae occurrant iis
quae in proxime sequentibus divisionis punctis curva ad an-
culos rectos insistunt, quales sunt linea BN, CO, DP; ut in-
quam subten sa quaque habeat ad sibi adjacentem curva per-
pendicularem, velut a B ad BN, BC ad CO, CD ad DP, ra
tionem majorem quavis ratione proposita.
Sit enim dataratio linex EF ad F C, quae recto anrulo ad F jun-
TantuI, e ducatur recta C F FT.
Incellisatur primo curra a B D in partes tam exiguas secta pun-
Ctis B, C, ut cansentes quae ad bina quaeque inter le proxima pun-
ctacurram contingune, occurrant libimutuo secundum angulos
qui linguli majores lint angulo F E. e; quales lune ansuli a X B,
BLC, CM D. Quod quidem tieri posse cridentius cs quam ut de-
monstratione indigeat. Ductis jam Tubrensis A B, BC, CD, _E CrC
etis currae perpendicularibus BN, CO, D P, quae occurrant produ-
ctis AK, BL, C M, in N, O, P: dicorationes lingulas rectarum,
aBadBN, B c adc0, CD ad D P, majores eAe raTIOMC PF Ad XC.