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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 433, page id 1041163592:0467
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11
LFBBA
crum B D demittanEUE sInUS FP. EE Cumma quadTAEOTUM EK YERXIOS
+33
PRINCIPIA MALHEMATICA.
rum ex rocidem semidiameto et.
Partes innumeras aequales, ec a parribus singulis sad diame.
Tinibus omnibus PY aequalis crie summae quadratorum ex sinibus
omnibus CT, et summa utraque aequalis erie summae quadrato
rum ex toridem lemidiameeris CP; adeoque summa quadrato.
rum ex omnibus FP, erie duplo minor quam summa quadrATO
Jam diridatur perimeter circuli AF in particulas eotidem x
quales, ex ab earum unaquaque sad planum e R demittatur
Derpendiculum FCr, uc de a puncto  perpendiculum AH. EL
vis qua particula lrecedit a plano _ R, erit ut perpendiculum
illud FC per hypochesin, de haec vis ducta in dictantiam CC1)
erit efficacia particulae Fad Terram circum centrum ejus con-
vertendam. Adeoque efficacia parriculxe in loco F erit ad CAi-
caciam particula in loco A, uE FC ZGC 2d ATTXFTC, hOC
eAt, uE FCg ad ACg; et propterca efficacia cora particularum
omnium in locis luis F, erit ad efficaciam parricularum eotidem in
loco A, ut summa omnium FC g ad summam eoridem AC. 9, hoc
est, (per jam demonstrata) ut unum ad duo. 9. F. D.
EF quoniam particulae agunt recedendo perpendicularicer a
plano e R, idque aequaliter ab ueraque parte hujus plani: caedem
converrent circumterentiam circuli sEquatoris, cique intaerentem
Terram, circum axem tam in plano illo _ R quam in plano Ai qua-
toris jacentem.
KKK
L. F. HI.
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