Select parts of Saunderson's Elements of algebra : for the use of students at the universities.

  • Nicholas Saunderson
Date:
1776
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Licence: Public Domain Mark

Credit: Select parts of Saunderson's Elements of algebra : for the use of students at the universities. Source: Wellcome Collection.

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    that the extremes will be proportionable, that is, that Po a--b will be to a—b as c-l-d is to c—d. ’ Thirteenthly, if there be a feries of numbers, 4, J, m,n, whereof &.is to] as ato b, and / to mas cto d, and mto nase tof; I fay then that & the firft term will be to the laft, as ace the produ@ of all the other antecedents to 2 df the produc of all the other confequents: for kis to 1 as @ to ’, by the fuppo- fition; and we fhall find that aistodasacetobce — by multiplying extremes and means; therefore & isto /asacetodce; and for a likereafon/ is tomas bce to bde, and m isto as bde to bdf; therefore, ex aque, kistonas ace to bdf. ? Of the extraction of the /quare roots of fimple algebraic quantities. 17. The extraction of the fquare root of fimple al- — gebraic quantities is fo very eafy, that it needs not to be infifted on. Thus the fquare root of aa is-}-or—a, the fquare root of gaa is-+-or—3a, and that of 4aabb is-t-or—2ad: this is plain from the definition of the - {quare root; for the fquare root of any quantity, fup- pofe of 4aabb, is that which, being multiplied into itfelf, will produce 4246: now—2a) multiplied into” itfelf will produce 42a, as well as-++-2a), and there- — fore one quantity 1s as much its fquare root as the - other. When the fquare root of a quantity cannot be ex- tracted, it is ufual to ficnify it by this mark »/: thus / 20a fignifies the fquare root of 24a; thus Waq—~4b — fignifies the {quare root of the whole quantity aa—ab; : a—4b | thus —* fignifies a fraGtion whofe numerator is — 2 the {quare root of the whole quantity 2za—4b, and 400—a> ——— fignifies 124 of whofe denominator is 2a; thus 7 2 the |
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