Prop. LXXXI. Prob. XLI.
*Stantibus jam positis, mensuranda est Area*ABNA*.*
A puncto P ducatur recta PH Sphæram tangens in H, & ad axem PAB demissa Normali HI, bisecetur PI in L; & erit Page 207 (per Prop. 12, Lib. 2. Elem.) PEq. æquale PSq. + SEq. + 2PSD. Est autem SEq. seu SHq. (ob similitudinem triangulorum SPH, SHI) æquale rectangulo PSI. Ergo PEq. æquale est contento sub PS & PS + SI + 2SD, hoc est, sub PS & 2LS + 2SD, id est, sub PS & 2LD. Porro DE quad. æquale est SEq. - SDq. seu SEq. - LSq. + 2SLD - LDq. id est, SLD - LDq. - ALB. Nam LSq. - SEq. seu LSq. - SAq. (per Prop. 6 Lib. 2. Elem) æquatur rectangulo ALB. Scribatur itaq; 2SLD - LDq. - ALB pro DEq. & quantitas {DEq. × PS} ÷ {PE × V}, quæ secundum Corollarium quartum Propositionis præcedentis est ut longitudo ordinatim applicatæ DN, resolvet sese in tres partes
| 2 SLD × PS | - | LDq. × PS | - | ALB × PS | : |
|---|---|---|---|---|---|
| PE × V | PE × V | PE × V |