Page:The Algebra of Mohammed Ben Musa (1831).djvu/205

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.

( 189 )

मूलं गुणार्धेन युतं विहीनं

वर्गीकृतं प्रष्ठुरभीष्ट राशिः ११

i.e. rendered literally into Latin:

Per multiplicatam radicem diminutæ [vel] auctæ quantitatis

Manifestæ, additæ ad dimidiati multiplicatoris quadratum

Radix, dimidiato multiplicatore addito [vel] subtracto,

In quadratum ducta-est interrogantis desiderata quantitas.

The same is afterwards explained in prose:

यो राशिः स्वमूलेन केनचित् गुणितेन उनो युतो वा दृष्टस्तस्य मूलस्य गुणार्धकृत्या युक्तस्य दृष्टस्य यत् पदं तद्गुणार्धेन युतं यदि मूलोनो दृष्टो राशिर्भवति यदि गुणमूलयुतो दृष्टस्तर्हि विहीनं कार्य तस्य वर्गो राशिः स्यात् ११

i.e. “A quantity, increased or diminished by its square-root multiplied by some number, is given. Then add the square of half the multiplier of the root to the given number: and extract the square-root of the sum. Add half the multiplier, if the difference were given; or subtract it, if the sum were so. The square of the result will be the quantity sought.” (Mr. Colebrooke’s translation.)

Feizi’s Persian translation of this passage runs thus:

هرگاه شخصي عددي را مضمر کرد و جذر او را يا كسري