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36
De Extractione Radicum vantitatum
§. 40. Tabula Dignitatum, eller Tafla, som utwisar Digniteterna af de enkla naturliga Talen.
Xad. | Qvd. | Cub | 4 Dig. | 5 Dig | 6 Dig. | 7 Dig |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 4 | 8 | 16 | 32 | 64 | 128 |
3 | 9 | 27 | 81 | 243 | 729 | 2187 |
4 | 16 | 64 | 256 | 1024 | 4096 | 16384 |
5 | 25 | 125 | 625 | 3125 | 15265 | 78125 |
6 | 36 | 216 | 1296 | 7776 | 46656 | 279936 |
7 | 49 | 343 | 2401 | 16807 | 117649 | 823543 |
8 | 64 | 512 | 4096 | 32768 | 262144 | 2097152 |
9 | 81 | 729 | 6561 | 59049 | 531441 | 4782969 |
§. 41. Regula Generalis De Extrahendis
Omnium, Simplicium Dignitatum Radicibus.
a | b | Dignitas Prima | ||||
a2 | 2ab | b2 | 2:da | |||
a3 | 3a2b | 3ab2 | b3 | 3:tia | ||
a4 | 4a3b | 6a2b2 | 4ab3 | b4 | 4:ta | |
a5 | 5a4b | 10a3b2 | 10a2b3 | 5ab4 | b5 | 5:ta |
a6 | 6a5b | 15a4b2 | 20a3b3 | 15a2b4 | 6ab5 | b6 |
a7+7a6b+21a5b2+35a4b3+35a3b4+35a2b5+7ab6+b7=7:ma | ||||||
a8+8a7b+28a6b2+56a5b3+70a4b4+56a3b5+28a2b6+8ab7+b8=8:va | ||||||
a9+9a8b+36a7b2+84a6b3+126a5b4+126a4b5+84a3b6+36a2b7+9ab8+b9=9:na | ||||||
a10+10a9b+45a8b2+120a7b3+210a6b4+252a5b5+210a4b6+120a3b7+45a2b8+10ab9+b10=10:ma |
§. 42.