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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 91, page id 797435492:0319
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L RC F.
XI:
R. FZ; erie spatium A D L. K aequale rectangulo Cx R, B DB.
Nam (IE P) EI == R, e compleatur rectangulum BDHI; cum
aumPTA M N indefinite ParVZ CUrVX A B parricula dueantur NC 2d
BD; SEMEX, HOS ad AD parallelX. FAque HO. MO::
TE. FM:: R. EZ. OndCNOXFZ ==MO XR, hoc eA FC
XFZ = FSx BX. ergocum omnia rectangula F C. X FZ minime
differant a SPaTIOADLR; Se omnia toridem rectangula ES X F X
componant rectansulum DHI LB, Cacis liquer Propolitum.
ZX. Tildem positis, sIE Curra P Y O talis, ut sumpea in sumpea
recta MI X ordinata F. X (respectirae) ip(i FZ aquetur, exit Cumma
quadratorum ex FZ (ad rectam A D compurata) par ci quod HC ex
ipCa R in spatium DB QB ducta.
Fst enim BO. ES :: AO. MO:: RX FZ, FZG:: RXFY.
FZ 9. ad eoque F C X FZ G = FSXR X B Y.
LXI. Simili ratione summa Cuborum ex FZ aequatur ei quod Hc Cx R
in summam quadrarorum ex rectis F. Y ad B D applicatis neque non (I.
mili quoad reliquas poteltates tenore.
ZXII. Sit curra quaeris DOR, in qua designarum punctum D;
e subrensa recta DR; Sit item curra A F calis, ut a D projecta qu’a
vis recta D M F (quae curvas secer punctis M, F) duetisque DS ad
DMInormali, _ MS Curram DO R tangente (concurrentibus uriq;
puncto 5) dataque quadam R, SItD S. 2 R:: DM9. DF q; erit
sparium AD F X qualC Ex R, DR.
Nam subtensa D K indefinire secta concipiatur punctis PO, _C.
Per gu centro C descripri tran (eanE aECUS P M, O RN; curram
DOK secanceS plnCtiS M, HI; per quae ducantur rectae DMF,
DNO; SINEVerOD Tad DR; _ DS ad D M perpendiculares;
quibus Occurrant ranSenteS R T, M S. demum centro D per P duca-
tur arcus F X; _ per P arcus I Y. Tam, ob sectionem indetinitam,
estrriangulum R P M triangulo K D T Cimile. ac ided MP. PR::
TD. DR. ITEM CADP. P M :: DB. EX. Peu propter altigna-
eam Causam, DK. MP :: DF. PX. FR itaGUE MPX DR. PK X
MP:: TDXDE. DRX E X. HOC CA DR. PR:: TDKDE9.
DR X EX XDE. AC IndE DR G XEXZDF = PRX ID X
DF g. (a) FCantCMDT. 2R :: DR9. D E9; SeNDPXDFG (a) HyP
== 2 R X D R g. CrGOCADRGK F Z XDF == PR X ZR XDR9.
Quare F X X D F == 2 R X P R; hOC CA, 2 sCCTOFD F X =L 2R XP R.
unde sectOE D E X == R X P R. Simili plano discursu sectOF D F Y
rQuatuX
F18. 1280