Full text: Clavius, Christoph: Geometria practica

LIBER OCTAVVS. bum ponitur differentia, qua à præcedenti cubo differt. In quarta denique co-
lumna ſcribantur ordine cuborum radices.

416.1.

Differentiæ
cuborum quo
modo repe-
riantur.
Conſtructio
tabulæ cubo-
rum.
Progreſſio \\ ſenarij. # Differẽtiæ \\ cuborum. # Cubi. # Radices.
6 # 1 # 1 # 1
12 # 7 # 8 # 2
18 # 19 # 27 # 3
24 # 37 # 64 # 4
30 # 61 # 125 # 5
36 # 91 # 216 # 6
42 # 127 # 343 # 7
48 # 169 # 512 # 8
54 # 217 # 729 # 9
60 # 271 # 1000 # 10
66 # 331 # 1331 # 11
72 # 397 # 1728 # 12
78 # 469 # 2197 # 13
84 # 547 # 2744 # 14
90 # 631 # 3375 # 15
96 # 721 # 4096 # 16

Eædem differentiæ cuborum in ſecunda columna deſcriptæ inuenientur
quo que hoc modo. Radicis propoſitæ quadratum triplicetur, addaturq; radix
triplicata, atque inſuper 1. Conflatus enim numerus erit differentia, qua cubus
propoſitæ radicis ab inſequenti cubo differt. Vt ſi deſideretur differentia inter
cubum 216. radicis 6. & cubum proximè maiorem. Quadratum radicis 6. eſt 36. triplum eius eſt 108. cui ſi addatur triplum radicis, videlicet 18. & inſuper vnitas,
conflabitur differentia 127. quæſita. Atque hoc modo, ſi continuentur differen-
tiæ cuborum ope progreſsionis ſenarij, extendetur tabula cuborum, quantum
libuerit. Suntautem, vt vides, numeri progreſsionis ſenarij ſextupli radicum cu-
borum, ſinguli ſingularum. Vt 60. ſextuplus eſt radicis 10.

Qvia verò diximus, cubos gigni ex ad ditione numerorum imparium, nimi-
rum primum eſſe 1. ſecundum ex duobus ſequentibus 3. 5. confici, & tertium ex
tribus ſequentibus 7. 9. 11. & c. ita vt quilibet ex tot imparibus coaceruetur,
quotvnitates in eius radice continentur; ſi curioſus quiſpiam noſſe deſideret,

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