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]

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[4.38.] An rectè phyloſophiœ penus Ariſtoteles ſenſerit de loco im-pellendo à pyramide. CAP. XXXVIII.
Page: 208 (196)
[4.39.] Examinatur quam ualida ſit ratio Aristotelis de inalterabilitate Cœli. CAP. XXXIX.
Page: 209 (197)
[5.] IN QVINTVM EVCLIDIS LIBRVM
Page: 210 (198)
[Item 5.1.]
Page: 210 (198)
[5.1.1.] Horum autem primum est.
Page: 210 (198)
[5.1.2.] SECVNDVM.
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[5.1.3.] TERTIVM. Quę est εuclidis ſeptima propoſitio.
Page: 210 (198)
[5.1.4.] QVARTVM. εuclidis uerò nona propoſitio.
Page: 211 (199)
[5.1.5.] QVINTVM. Euclidis uerò octaua propoſitio.
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[5.1.6.] SEXTVM. εuclidis uerò decima propoſitio.
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[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
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[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
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[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
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[5.1.10.] DECIMVM.
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[5.1.11.] VNDECIMVM.
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[5.1.12.] DVODECIMVM.
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[Item 5.2.]
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[5.2.1.] THEOR.I. II. ET III.
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[5.2.2.] THEOREM. IIII.
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[5.2.3.] THEOR.V. ET VI.
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[5.2.4.] THEOR. VII. VIII. IX.X. XI. XII. XIII.
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[5.2.5.] THEOREM. XIIII.
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[5.2.6.] THEOR. XV.
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[5.2.7.] THEOREM. XVI.
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[5.2.8.] THEOR. XVII.
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[5.2.9.] THEOREM. XVIII.
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[5.2.10.] THEOREM. XIX.
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[5.2.11.] THEOREM. XX.
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[5.2.12.] THEOREM. XXI.
Page: 215 (203)
[5.2.13.] THEOREM. XXII. XXIII.
Page: 215 (203)
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215203IN QVINT. LIB. EVCLI. portio .a. ad .b. quæ eſt .c. ad .d. probabo ita ſe habituram proportionem .b. ad .a. ſicut
ſe habet .d. ad .c. hoc argumento: ſi .a. ad .b. ita ſe
habet ſicut .c. ad .d. ex .16. theoremate ita ſe ha
268[Figure 268] bebit .a. ad .c, ſicut .b. ad .d. Quare ſic ſe habebit
b. ad .d. ſicut .a. ad .c. Itaque ex eodem .16. ita ſe
ſe habebit .b. ad .a. ſicut .d. ad .c.
THEOREM. XX.
QVamuis .20. theorema apud Eucli. perfectè demonſtratum fuerit, poteſt ni-
hilominus & hac via demonſtrari. Sic ſe habeat proportio .a. ad .b. ſicut ſe
habet .c. ad .d. & proportio .b. ad .e. ſicut .d. ad .
f. Dico quod ſi .a. maius fuerit .e. pariter .c. maius
269[Figure 269] erit .f. & ſi .a. minus fuerit .e: c. quoque; minus erit
f. ſin verò ęquale, ent æquale erit. Nam ex pri
mo poſtulato certi ſumus ita ſe habere pro
portionem .a. ad .e. ſicut ſe habet proportio .c. ad
p. Quare ex .12. theor propoſitum manifeſtum erit.
THEOREM. XXI.
VIgeſimum primum theorema, ſatis apud Eucli. probatum, nihilominus præ-
ſcripto nunc modo demonſtrari poterit.
THEOREM. XXII. XXIII.
DVO hæc theoremata in primum poſtulatum collegimus.
Sequentia verò cum exactè apud Eucli. demonſtrentur non eſt cur nos in
ijs immoremur.

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