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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 271, page id 1040780814:0289
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AB
LIB. TII.
EE CTEOMETR FC A E, L EMEN FA.
27I
demictatur perpendicularis MIK; TUatUE D E aequalis P F, unde CH
aequalis CP, BE jUINSAEUF L H. OuOniaI APF CA FHIPIIS, CA (per
PrOp. XXI. LIB. T. FV. Conic.) CPg ad ML. g ut rectansulum sub a C 8
CF. ad rectangulum suD AM _E MF: FE, per eandem, in circulo AFB
eAt CFg ad MDg etiam ut rectansulum (ub AC _ CF ad rectan-
sulum sub AM eEMF; _ idco CFg erit ad MD9 SiCut CPG ad M L. 9.
Inde cF est ad MD SIcut CP ad MF; adeoque (per PrOP. XIX. Fl. V.)
eF CA ad L. D fICUE CP ad MZ; hoc eAt, ED CH ad L. D HICUE CH ad
ML; _ isitur (DeF PrOP. IT. FL. VT.) LI parallela eAt ad CM; _E prO.
inde triangulum L DE limile criangulo MD C,  Similiter POSEUM.
A trianguli autem cm D angulo recto n dueta est ad hypochenulam
De perpendicularis recta MK, quod etiam quamproxime factum eAt
in triansulo HIT D, existente curra Reliptica particula LD e terc
recta, _ ad CD normali, DFODter FIip(IM AP EP non multum ablu.
dentem à circulo APPC: Onde cD similiter dividitur in X atque
ED in B dirila CA; id cAt, H D est ad DB Sicut CD ad DV, SIVC P F ad
BD SICUE CD ad DK. RUESUS, proPter triangulum rectangulum CMD
divisum per rectam Mx ad eo normalem (per PrOP. VII. Fl. VL.)
CTUNL CD, DM, DE proportionales, sire ratio cD ad Du duplicata ra-
tionis cD ad DM; hoc cA, rationis cF ad ND. Sed hactenus cA
ostentum esse PF ad BD Licut cD ad DK; e isitur PF CA ad BD in
duplicata ratione CF ad MD: Sed CF CA FInUS FOTS, _E MD SInUS
rectus anguli acB, nempe Latitudinis lociB; _ DF, BD Tunt incre.
menta scaritatis vel lonsitudinis penduli dato tempore olcillantis
locis Pe B congrua, supra graritatem pendutire lonoitudinem ad
Aiquatorem: Ft isitur, polica aP F. P FIlipCI, incrementum srari
tatis vel lonsitudinis penduli ad Polum, supra sraritatem pendu.
lire lonsitudinem ad AEquatorem, est ad Timile incrementum in
alio quoris superficiei Terrae loco B quamproxime in duplicata Pa-
tionc radii ad sinum rectum Latitudinis dicti loci B. Aeque idem
ostendetur de alio quoris loco in Terra superticie: Ft isitur, ex
aquo, si a P F. P Fuexit F. IlipSis, erunt graritatis pendulive longicudi-
nis incrementa in dirertis locis Cuperticiei Terra, Tupra gravitatem
pendulire pari tempore oscillantis longicudinem ad Aiquatorem,
in duplicata ratione sinuum rectorum Latitudinum ictorum loco.
TUm QUaMPTOXIIO.
SCHOLTOM.
Pramissa omnia vera sunt ex hypothesi quod Terra ex materia
uniformi e aequidensa constat. Supposuimus enim Auidum, quo
canales acP, B CP impleti sunt, uniforme esse de homogeneum. Ve-
rum limateria, ex qua Terra constar, densior sit ad centrum quam
versus superticiem, praedicta incrementa distantiorum a centro ver-
sendo a Polis ad Aiquatorem, nisque proportionalia incrementa
sraritatis lonsicudinisque penduti dato tempore olcillantis per-
Sendo ab LR. quatore ad Polos, majora erunt quam pro calculo suve.
rioribus innixo; ex Terra Axis minor erit relpectu Diametrorum ci
dem normalium. Nam s materia ilta vertus centrum, qud Terra