Petri Philomeni de Dacia in algorismum vulgarem Johannis de Sacrobosco commentarius. Una cum algorismo ipso edidit et praefatus est Maximilianus Curtze.
68 cum ultimo resultant 36, qui est numerus par. Per medietatem (ergo) eius, scilicet per 18, multiplicentur loca positionum, scilicet 7, et proveniunt 126, summa totius progressionis. Regula secunda est, quod, si ex primo numero et ultimo resultat 5 numerus impar, semper per illum multiplices medietatem numeri locorum sive positionum, et exibit summa in qualibet progressione. Verbi gratia: in progressione naturali sit hoc exemplum. Primo: 1. 2. 3. 4. 5. 6. 7. 8. Hic sunt octo loca positionumn, et numerus aggregatus ex prirno et ultimo est 9. Due igitur 9 in medietatem de 8, scilicet in 4, et evenient 36, summa pro10 gressionis. Vel sic: 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. Hic sunt loca 10 positionum, et aggregatum ex primo et ultimo est 25. Duc igitur medietatem locorum, scilicet 5, in 25, et provenient 125, (summa totius progressionis). Aliud exempltm in progressione intercisa esse potest illud: 1. 4. 7. 10. 13. 16. Hic 15 sunt 6 loca positionurn, et numerus aggregatus ex primo et ultimo fit 17. Hunc ergo multiplices per medietatem locornm, scilicet per 3, et provenient 51, (summa totius progressionis). Vel sic: 3.8.13. 18.23.28. Hic sunt 6 loca positionum, et ex primo et ultimo resultant 31. Hunc ergo multiplices per me20 dietatem locorum, scilicet per 3, et provenient 93, summa totius progressionis. Unde debes hic indubitanter scire, quod vel numerus locorum erit par, vel numerus aggregatus ex primo et ultimo erit par, vel uterque. SPECIES NONA, SCILICET DE RADICUM EXTRACTIONE. 25 Sequitur de radicum extractione etca. Haec est nona species et ultima huius operis, in qua facit auctor duo. Primo enirn praemittit capitulum quoddam praeambulum, in quo tangit quaedam, quorum cognitio est necessaria ad hanc speciem, et secundo de intento prosequitur, cum dicit: Si velis igitwur, iuxta 30 principium capituli sequentis, ubi alii aliud capitulum assignaverunt. Adhuc primo praemittit ea, quae declaranda sunt ad intentum principale, et secundo ea pertractat, cum dicit: Prae
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About this Item
- Title
- Petri Philomeni de Dacia in algorismum vulgarem Johannis de Sacrobosco commentarius. Una cum algorismo ipso edidit et praefatus est Maximilianus Curtze.
- Author
- Sacro Bosco, Joannes de, fl. 1230.
- Canvas
- Page 60
- Publication
- Hauniae,: A. F. Host,
- 1897.
- Subject terms
- Arithmetic
Technical Details
- Link to this Item
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https://name.umdl.umich.edu/acv7283.0001.001
- Link to this scan
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https://quod.lib.umich.edu/u/umhistmath/acv7283.0001.001/89
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The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].
DPLA Rights Statement: No Copyright - United States
Related Links
IIIF
- Manifest
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https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acv7283.0001.001
Cite this Item
- Full citation
-
"Petri Philomeni de Dacia in algorismum vulgarem Johannis de Sacrobosco commentarius. Una cum algorismo ipso edidit et praefatus est Maximilianus Curtze." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acv7283.0001.001. University of Michigan Library Digital Collections. Accessed June 1, 2025.