Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Table of figures

< >
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[Figure 137]
[Figure 138]
[Figure 139]
[Figure 140]
[Figure 141]
[Figure 142]
[Figure 143]
[Figure 144]
[Figure 145]
[Figure 146]
[Figure 147]
[Figure 148]
[Figure 149]
[Figure 150]
[Figure 151]
[Figure 152]
[Figure 153]
[Figure 154]
[Figure 155]
[Figure 156]
[Figure 157]
[Figure 158]
[Figure 159]
[Figure 160]
< >
page |< < (100) of 445 > >|
112100IO. BAPT. BENED. a.b: c.d: e.f. et .g.h. quorum .a.b. et .g.h. nobis tantummodo cogniti ſint, ſitque imagina
tione deſcriptus cubus .a.q. primi termini, cubusque .d.k. ſecundi rermini, conſidere-
mus etiam baſim .a.i. quadratam ipſius cubi .a.q. hoc eſt præcedentem dignitatem ip
ſius cubi eiuſdem radicis, quæ quidem baſis .a.i. multiplicetur per quartum terminum
g.h. productum autem ſit .g.a. vnde eadem proportio erit .a.q. ad .a.g. quæ .b.q. ad .b.
g.
per .25. vndecimi, ſed per primam ſexti, vel .18. aut .19. ſeptimi ita eſt .q.i. ad .i.g.
vt .b.q. ad .b.g.
quare per .11. quinti
ita erit .a.q. ad .a.g. vt .q.i. ad .i.g. ideſt
155[Figure 155] vt .a.b. ad .g.h. ſed vt eſt .a.b. ad .g.h.
ſic eſt .a.q. ad .k.d. per .36. vndecimi,
ſeu per .11. octaui, vnde per .11. quin
ti ſic erit .a.q. ad .a.g. vt ad .k.d.
Qua-
re per .9. eiuſdem .a.g. ęqualis erit .k.
d
.
Vnde rectè erit accipere radicem
cubam .a.g. pro ſecundo termino .c.d.
id, quod nobis inſeruit ad inueniendam tertiam partem vnius propoſitæ propor-
tionis.
THEOREMA CL.
Sed vt ſpeculatio iſta ita vniuerſalis fiat vt ad oens dignitates applicari poſſit;
Supponamus .a.q. et .k.d. eſſe duas dignitates quas volueris vnius, ſed eiuſdem
ſpeciei, et .a.i. dignitas præcedens dignitatem .a.q.a. cuius multiplicatione in .a.b.
eius radix producitur dignitas .a.q. & ab ipſius .a.i. multiplicatione in .g.h. reſultet .a.
g.
vnde ex .18. vel .19. ſeptimi eadem proportio erit .a.q. ad .a.g. quæ .a.b. ad .g.h. ſed
eadem etiam eſt .a.q. ad .k.d. ex ijs, quæ in .17. theoremare dixi, vnde ex .11. quinti,
ita erit .a.q. ad .a.g. vt ad .k.d.
Quapropter .a.g. æqualis erit .k.d. & ideo cum inuenta
fuerit radix huiuſmodi dignitatis ex quantitate .a.g. habebimus .c.d. ſecundum ter-
minum quæſitum.
THEOREMA CLI.
Vnde verò fiat, quòd cum quis voluerit dimidium alicuius datæ proportio-
nis inuenire, rectè faciat, ſi accipiat radices quadratas illorum datorum rer-
minorum, etſi voluerit tertiam partem, accipiat radices cubas:
ſi autem quartam,
accipereradices cenſicas cenſicas ipſorum, & ſic de ſingulis in .17.
Theoremate om-
nia patent.
THEOREMA CLII.
Vnde autem fiat, vt cum quis voluerit multiplicare aliquam proportionem
per fractos, rectè faciat prius multiplicando eam per numeratorem, dein-
de productum diuiſerit per denominationem ipſorum fractorum.
Vt exempli gratia, cum aliquis voluerit multiplicare proportionem ſeſquiquar-
tam per duo tertia, multiplicabit prius ipſam proportionem per numeratorem .2.
& productum, erit proportio .25. ad .16. qua poſtea diuiſa per .3. denominatorem,
prouentus erit proportio radicis cubæ .25. ad radicem cubam .16. vel vt proportio.

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index