165145LIBER II.
ipſi, CX, æquidiſtans ad ſibi homologam in figura, ΠΩ, ipſi, ΩΛ,
æquidiſtantem, vel quælibet in quacunque figurarum ipſi, BC, in
ſolido, AP, æquidiſtantium, ad ſibi homologam in ſolido, V &
lgitur ſimilia ſolida ſunt in tripla ratione linearum, vel laterum ho-
mologorum, quæ ſunt in eorundem homologis figuris, quod nobis
oſtendendum erat.
æquidiſtantem, vel quælibet in quacunque figurarum ipſi, BC, in
ſolido, AP, æquidiſtantium, ad ſibi homologam in ſolido, V &
lgitur ſimilia ſolida ſunt in tripla ratione linearum, vel laterum ho-
mologorum, quæ ſunt in eorundem homologis figuris, quod nobis
oſtendendum erat.
COROLLARIVM I.
_E_T quia iam dicta ſimilia ſolida oſtenſa ſunt eſſe in tripla ratione li-
nearum bomologarum, quæ ſunt in homologis figuris, æquidiſtan-
tibus oppoſitis planis tangentibus vtcunque ſumptis, ideò clarum eſt ea-
dem ſimilia ſolida eſſe in tripla ratione quarumuis homologarum in ipſis
ſolidis deſoriptibilium, & duas quaſuis homologas ſumptas iuxta quæ-
dam oppoſita tangentia plana, eſſe vt duas quaſuis homologas ſumptas
iuxta alia oppoſita tangentia plana.
nearum bomologarum, quæ ſunt in homologis figuris, æquidiſtan-
tibus oppoſitis planis tangentibus vtcunque ſumptis, ideò clarum eſt ea-
dem ſimilia ſolida eſſe in tripla ratione quarumuis homologarum in ipſis
ſolidis deſoriptibilium, & duas quaſuis homologas ſumptas iuxta quæ-
dam oppoſita tangentia plana, eſſe vt duas quaſuis homologas ſumptas
iuxta alia oppoſita tangentia plana.
COROLLARIVM II.
_V_Niuersè inſuper habetur, ſi fuerint quatuor rectæ lineæ deinceps
proportionales, vt prima ad quartam, ita eſſe ſolidum deſcriptum
à prima ad ſolidum illi ſimile deſ criptum à ſecunda, & huius conuer-
ſim; dummodò deſcribentes ſint lineæ, vel latera homologa ſimilium fi-
gurarum, quæ in ipſis homologæ vocantur.
proportionales, vt prima ad quartam, ita eſſe ſolidum deſcriptum
à prima ad ſolidum illi ſimile deſ criptum à ſecunda, & huius conuer-
ſim; dummodò deſcribentes ſint lineæ, vel latera homologa ſimilium fi-
gurarum, quæ in ipſis homologæ vocantur.
THE OREMA XVIII. PROPOS. XVIII.
SI quaturor rectę lineę proportionales fuerint, ſolidum de-
ſeriptum à prima ad ſolidum ſibi ſimile deſcriptum à ſe-
cunda, erit, vt ſolidum deſcriptum à tertia ad ſibi ſimile de-
ſcriptum à quarta. Et ſi fuerint quatuor ſolida proportiona-
lia, quorum quæ ſunt eiuſdem proportionis termini ſint ſimi-
lia, eadem deſcribentia erunt proportionalia; dummodò ta-
men ſemper deſcribentia ſint vel lineæ, vel latera homologa
figurarum, quæ in ipſis homologæ vocantur.
ſeriptum à prima ad ſolidum ſibi ſimile deſcriptum à ſe-
cunda, erit, vt ſolidum deſcriptum à tertia ad ſibi ſimile de-
ſcriptum à quarta. Et ſi fuerint quatuor ſolida proportiona-
lia, quorum quæ ſunt eiuſdem proportionis termini ſint ſimi-
lia, eadem deſcribentia erunt proportionalia; dummodò ta-
men ſemper deſcribentia ſint vel lineæ, vel latera homologa
figurarum, quæ in ipſis homologæ vocantur.
Sint ergo quatuor rectę lineę proportionales, AB, CD, FG, H
M, & ſint ab ipſis, AB, CD, deſcripta ſimilia ſolida, AXB, CV
D, & ab, FG, HM, ſimilia ſolida, OFPG, NHQM, ita vt
duæ, AB, CD, ſint homologę figurarum, AEBY, DKC ℟, &
M, & ſint ab ipſis, AB, CD, deſcripta ſimilia ſolida, AXB, CV
D, & ab, FG, HM, ſimilia ſolida, OFPG, NHQM, ita vt
duæ, AB, CD, ſint homologę figurarum, AEBY, DKC ℟, &