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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 92, page id 797435492:0320
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L E C T. ZXI.
aequatur ipsI R X RMI, vel R X OP. itaque torum spatium AD F
quod ab ejusmodi sectoribus minime diftere adxquatur rOri R XD R.
quod erar Propolicum.
XXIII. Tisdem, quoad exetera, positis atque paratis, duICantuFR FY
adKT, de MIad MS perpendiculares; ex concipiatur jam curra
A F nacura talIS, UF SIE D F = VDR ZDEI; _EDF = V D MX
DI; ac ita perpetuo; erir spatium A D E quadrati ex D R subqua
druplum.
Nam est M P. PR:: DK. DH:: DRg. DR X DHI:: DRG.
D Fg. IteM DP. PM:: DF. F Z; HOC CAEDR. PM:: DF.
FX. CrOOMP XDR. PKXPM:: D RGXDE. DEGXFX.
HOC est DR, PR :: D R g. D FXE Z. VEIDR g. DRXPR:: DR 9.
DE X EZ. unde DR X P R =D P X F X. Siili raTIONED MX MH
(VeIDF FDO) = DEX EY: VeTIM OINIa DR XPR, DP Z
P O, EEC. Eequantur semiss quadrati ex DR; _C OmHIADP X F Z,
DFX FY, SeC aequantur dupto spatio FD A; unde maniseste cOn-
Sequitur Propolitum.
XXIV. Sic curra quaepiam DOK, in qua punctum D; cuique
Tubtendatur recta DK; sic item curra DZ Lcalis, ut sumpro in curra
DOR puncto quopiam M, connexaque DM; ec duct a D S ad DM
perpendiculari, ecM S curram DO R tansente; sumpra demum
DP = DM, _ ducta P Z ad DK perpendiculari, (IE P L =DS;
erit spacium D R l aequale duplo spatio D ROD.
Nam recta RP concipiatur indetinite parra; _ DT ipsiDR per-
pendicularis (IE, _ R T Curram DOR tangat. FRiraque (ducto
AFCUM P) rurtuSRP. PM:: KD. DT:: RD. RI. undeRP X
RI = P M X RD. Capiatur alia particula P 9, _ CeNErO D Pex
ducatur arcus QN, quem secet lubren(aDM in R; est ergorur-
sUSMR. RN:: M D. DS; hocestP 9. RN:: MD. PZ qua
rePO XPZ =RNI XMD; ac ita continuo deinceps. Patet igitur
omnia limul rectangusa R P XR I, P OXPZ, QC. aequari aggrega
EO OmNium P MI Z RD, RNXMD, _cc. hoc est Epatium DR I
uplo spatiODRODXquari. 11
ZXV. lisdem quoad caetera policis arque paratis, ordinatae PL jam
aequales concipiantur ipsis M Srespectiris; ex ad rectam assumpram
XK, distancia sque XK, Zm, Xn, ec, aequales ipsis currae partibus
OOK, DOM, DON, _c. applicemu rectae k d, m d, n d, dc.
Pares
218. 228.
2
F1. +30.