Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.

PROBLEM II.

IN a right-angled ▵ having given the Hypothenusa and sum of the sides, to find the sides. E. g. If the Hypothenusa BC be given (Fig. 32.) and the sum of the sides CAB, to find the sides AB and AC separately, to form the Triangle.

SOLƲTION.

Make the Hypothenusa BC=a, the sum of the sides = b. Make one side e. g. AB=x, then will the other side AC be =b−x. Therefore

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Therefore according to Case 1. of affected Quadraticks. 〈 math 〉〈 math 〉 i. e. 〈 math 〉〈 math 〉 or 〈 math 〉〈 math 〉.

The Geometrical Construction. Having described a semi-circle upon BD=BC so a apply therein the equal lines BE and DE, and having described another semi-circle on BE apply therein BF=½b, to be prolonged farther out. Lastly, if another little semi circle be described at the ••nterval EF, the whole line AB

will be the true root or the side sought, and GB the false root, &c.

The Arithmetical Rule. From half the square of the Hy∣pothenusa substract the fourth part of the square of the given sum, and the root extracted out of the remainder, if it be ad∣ded to half the sum, will give one side of the Triangle; and substracted from the given sum, will give also the other Suppose e. g. BC to be 20, and the sum of the sides 28.