Valerio, Luca, De centro gravitatis solidorvm libri tres

List of thumbnails

< >
221
221
222
222
223
223
224
224
225
225
226
226
227
227
228
228
229
229
230
230
< >
page |< < of 283 > >|
1quadrupla igitur BC ipſius DK: cum igitur BC ſit
dupla ipſius KH, erit DK dimidia eiuſdem KH, & ſecta
bifariam KH in puncto D: ſed recta AG ſecabat eandem
KH bi fariam; per punctum igitur D tranſibit AG.
Quo­
niam igitur parabola ADC, cuius vertex D, ſeſquiter­
tia eſt per Archimedem trianguli ADB, cuius duplum
eſt triangulum ABG, ſicut & huius triangulum ABC;
triangulum ABC quadruplum erit trianguli ADB: qua­
lium igitur partium æqualium eſt triangulum ABC duo­
decim, talium erit triangulum ADB trium, & parabola
ADB, cuius ver­
tex D quatuor: du
plum igitur erit tri­
angulum ABC
mixtum parabolæ
ADB, cuius ver­
tex D, & cen­
trum grauitatis M:
ſed trianguli ABC
rectilinei eſt cen­
trum grauitatis N,
& F trianguli ABC
mixti; dupla igitur
erit MN ipſius N
F, & MD ipſius
163[Figure 163]
OF, & DN ipſius NO, propter ſimilitudinem triangulo­
rum: ſed & tota AN dupla eſt totius NG, ob centrum
grauitatis N rectilinei trianguli ABC; reliqua igitur AD
dupla eſt reliquæ GO. cum igitur AG ſit dupla ipſius
AD, quadrupla erit AG ipſiuſque GO. quare & quadru
pla AE ipſius FE ob parallelas: tripla igitur AF ipſius FE.
Rurſus quoniam ex Archimede ſeſquialtera eſt DM ipſius
MH, erit tota DH ad DM vt quinque ad tria, hoc eſt
vt decem ad ſex: ſed MD erat dupla ipſius OF; tota igi-

Text layer

  • Dictionary
  • Places

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index