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.

    101/432 page 91
    the product of the extremes mutt be equal to the product of the middle terms, Q, H. D The converfe of this propofition is allo true, ta wit, that Whenever we have an equation in numbers, wherein the product of two numbers on one fide is found’ equal to the product of two numbers on the other, fuch an equation may be refolved into four proportionals, by making the two numbers on either fide, the extremes ; and thofe on the other fi de, the middle terms: thus if ad= bc; by making a and d the extremes, and band ¢ the middle terms, we fhall have @ to 6as¢ to d: if this be denied, let abetobasctoe; then we fhall have ae== bc by the laft; but ad—= de by the fuppofition ; therefore Peper therefore ¢ ie d, and a istob as ¢ 1s to d. Q, E. D, - : NTO 6 “ois Gy: ' Whence if a, 6, and ¢, be continual proportionals, that is, if ais tob as@ is toc, we fhall have 6?=ae: and é¢ converfo, if °==ac, thena, 6, and ¢, will be continual proportionals, . The common properties of proportionality in numbers demonftraied, 16. From what has been delivered in the laft article, may be demonftrated ai] or moft of the common properties of proportionable numbers with a great deal of eafe, fome of the moft ufeful whereof I thall here throw together into one fingle article, for the reader to perule, either at prefent, or hereafter, as he . fhall fee occafion. Firft then, from what has been faid, may the rule ‘of three, which confifts in finding a fourth propor- tional, be moft diftinétly demonftrated: for let a, b and ¢ be three numbers given, in order to find d, a fourth elspa Mes fince aistod as ¢ is to d, you will have ad the product of the extremes, equal | ta
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