# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0152
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0152?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 118, page id 1041163592:0152
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=152
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000152.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.91
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

MMIIIIIII
18
PFTTEOSOPMLSE NATVRALIS
DE MorD puncta B, c perpecuo tangune; deque puncto V ad lincam AC eri-
ratur perpendiculum Va d abseindens areas currilineas V Dba
Dcd. e erigantur etiam ordinatae F.2, L.x: quoniam rectan-
oulum D b X IN CCu D b Z F. aequale est dimidio rectanguli
AXKN, scu triangulo FCK; e rectangulum D C X Y N Peu
DCx F. aequale est dimidio rectanguli Y L X XC, seu triangulo
XCT; hoc cA, quoniam arearum V D ba, VY C aequales semper
Cune nascentes particulae Db~ F, YC R, _ arcarum V D Cd,
VCX aequales temper unt nalcentes particulae DCX F, XCY,
erit area genita V Dba aequalis areae genitae VIC, adcoque cem-
Pori proportionalis, et arca genita VDcd aequalis Scctori se-
nito VC X. Dato isitur tempore quoris ex quo corpus dilcel-
sit de loco V, dabitur area ipsi proportionalis V D b as e inde
dabitur corporis alticudo C D vel CI; de arca V Dcd, eique
aequalis Sector VC X una cum ejus ansulo VCI. Datis autem
angulo VCP ex altitudine CP datur locus L, in quo Corpus com-
Pleco illo tempore reperietur. 8. F. I.
Corol. L. Ilinc maximae minimae que corvorum alticudines, id cAt
Aplides Trajectoriarum expedice inveniri pollunt. Sunt enim
ApSides puncta illa in quibus recta TC per cenerum ducta incidit
perpendiculariter in Trajectoriam VIK: id quod tic ubi rectae IR
ec NVX aequantur, adeoque ubi arca AB F D aequalis CA L. L.
Corol. 2. Sed e angulus RY N, in quo Trajectoria alibi secat
lineam illam YC, ex data corporis alcitudine IC expedice inveni-
cur; nimirum capiendo sinum ejus ad radium ut R N ad IK, id
CA, UE Z ad latuS quadeatum arcae  B F D.
Corol. 3. Si centro C _ vertice principali V describatur Sectio quae-
libCE COniCa V R S, e a quoris ejus puncto R a92EUF PangenS R Y
occurrens axi intinite producto CV in puncto T; dein juncta CR
ducatur recta C P, quae aequalis sic abscise C P, angulum que VC F
Sectori VC R proportionalem constituat; tendat aurem ad centrum C
Vis centriveta C ubo dictantia lOCOrum a CCNErO RCCIPYOCC PEODOE
tionalis, s exeat corpus de loco V justa cum Velocitate secundum
lincam rectae CV perpendicularem: progredietur corpus illud in
Prajectoria quam punctum P Perpetuo cansiE; adeoque s Conica
sectio CV R S HIyperbola sic, descender idem ad cenerum: Sin
Ca Fllip(S AE, ascendet illud perpecuo e abibie in infinieum. EE COn-
tra, si corpus quacunque cum Velocirare exeat de loco V, ec perin-
de ut incaeperie vel oblique descendere ad cenerum, vel ab c0 ob-
lique
WNIIIHS HIITMEHIIIHBIEE BIBHHBHBMIIIBIINBIBSHIMIIIIIBII N PAIIMSI. MIIIIII
LORPORO