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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 78, page id 898203430:0106
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=106
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VINCEHTIT VIVTANT DE LOCIS SOLIDIS
idem B C; ductoque in data B A ex vertice B quocunque raIO B A,
cui ex A CI normulis A F. Dico Semiordinatam pet A, seu D F, in
Parabola C F, normali AF aequalem esse.
Ob rectum enim angulum B A F, EE DEFPCM
dicularem A D super D F, est rectansulum
FDB aequale quadrato AD, cui, ob Parabo-
Ir. P Jam aequatur a quoque rectangulum C BD,
ergo rectangulum F. D B rectangulo C BD aequa-
le est, quare ob communem ipsorum alcicudi
nem BD erit recta F D aequalis C B, d qua
dratum FD quadrato CB aequale; quadracum
autem AD equale est rectansulo DBC, ereo
duo simul quadrata F D, D A, Sive vnicum
quadratum AF duobus simul, hoc Cst FCCLAM.
sulo CBD cum quadrato C B, vel vnico re-
ctangulo D CB aequale eric, sed de quadratum
ED (ob Parabolam C F.) aequale est cidem
rectangulo D CB, quum potium ( C B ejus rectum latus: OuarC qu I-
dratu E. D quadratO AF, _ TCCTA F D rectae AF aequalis cst, de sIC
de singulis dec. Ouod erat demonstrandum.
C O R O L L
nOnstat ex hac, in Parabola, semper alticudinem normatis sUPex ra-
mum ex verrice ductum recto lateri datae Parabola aequale este.
Oltensum est enim axis segmentum DF, quod est alticudo normalis AP
super ramum BA, aequale recto lateri BC.
P R OPOSt11O
22a2c212 a
NV Ellipso oblonca. Limes Ordinationis normalium
super ramos ex vertice ductos crectarum est ad Lo
cum concauum alterius Fllipsis oblonea per oppositum
verticem sibi circumsoriptae; cujus rectum latus datae
recta sit aequale, transuersum vero sit tertia proportio
nalis post differentiam laterum datae FllipsiS, (5 tran-
suersum ejusdem.
NTT FssipAiS oblonga AB, CUIUS verTeX B, trantuertus axis maiOr BD,
a ee rec um latus BF. ad B concingenter applicatum, sumaturque D6
terria proporcionalis post disserentiam inter lacera D B, B F, X lauS
DB, d Circa axeIM Tran(versum DC, cum recto latere ipS BF equali
descripra si Flliplis CFD. Dico hanc esse Limirem Ordinationis propo
sitae;
GonIC.