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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7563THEOREM. ARIT. ras confideranti ſpeculari licebit, Diametros harum figurarum notaui literis ſiue
characteribus .a.e.i.c.u.n.

103[Figure 103]

104[Figure 104]

THEOREMA XCV.

IN progreſſionibus, quæ ab alio termino quam vnitate incohantur, idipſum vt
monuimus accidit, hoc tamen notato, quòd ex conſequenti quælibet pars dia-
metri parallelogrammi, minimo termino æqualis erit, prout in progreſſionibus quæ
ab vnitate originem ducunt, ſingulæ partes diametri, vnitati ſui primi termini æ-
quales ſunt. At in reliquis progreſſionibus, vt in figura patet, eadem eſt propor-
tio totius diametri ad .o.n. quæ minimi termini ad vnitatem ex .13. quinti, nempe .
a.o. ad .o.n. vt .n.n.n.n. ad .n. In eiuſmodi progreſſionibus accidit quoque parallelo-
grammum à diametro in tres partes diuidi, quarum vnam ipſe occupat, reliquæ ve-
ro inter ſe æquales ipſum ambiunt. Ex quo illud etiam ſequitur, productum .a.o. in
dimidium .o.n. æquale eſſe dimidio parallelogrammi, quod minus eſt ſumma progreſ-
ſionis dimidio diametri, quod dimidum ſi inuenire voluerimus, minimum terminum .
n.n.n.n. per dimidium .o.n. multiplicabimus, & ex .18. aut .19. ſeptimi ipſum habe-
bimus, quandoquidem minimo termino per totum .o.n. multiplicato profertur integer
diameter ex .20. prædicti. Etenim vt diximus, eadem eſt proportio totius diame-
tri ad .o.n. quæ minimi termini ad vnitatem. Ita etiam dico ex dicta .20. ſeptimi.
idem dimidium diametri oriri, ſi quis dimidium minimi termini nempè .n.n. per to
tum .o.n. multiplicauerit. Quamobrem qui ſtatim ſummam propoſitæ progreſſionis
cognoſcere voluerit,

105[Figure 105] ſemper primum termi
num .n.n.n.n. cum .a.o.
coniunget, qua ſumma
per dimidium .o.n. mul-
tiplicata, aut .o.n. per
dimidium dictæ ſum-
mæ, ex prædictis rationibus propofitum conſequemur.

THEOREMA XCVI.

CVR ſi quis numerum terminorum inuenire velit, cognitis tantummodo pri
mo atque vltimo, rectè vltimum per primum diuidet, ex quo proueniens

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113	101
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Scan	Original
101	89
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106	94
107	95
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110	98
111	99
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113	101
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115	103
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117	105
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101	89
102	90
103	91
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106	94
107	95
108	96
109	97
110	98
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114	102
115	103
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