# Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and Geometry, in Their Relations and Uses

Orr and Smith, 1836 - 496 σεκΏδερ

### ‘ι κίμε οι ςώόστερ -”ΐμτανγ ξώιτιξόρ

Ρεμ εμτοπΏσαλε ξώιτιξίρ στιρ σθμόηειρ τοποηεσΏερ.

### –εώιεςϋλεμα

 SECTION I 1 SECTION II 17 SECTION III 30 SECTION IV 42 SECTION V 65 SECTION VII 118 THE FACTORS 127 SECTION VIII 147
 SECTION IX 171 SECTION XI 207 CONTENTS 219 SECTION XIII 264 SECTION XIV 301 SECTION XV 347 SECTION XVI 375

### Ργλοωικό αποσπήσλατα

”εκΏδα 396 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.
”εκΏδα 473 - Prove it. 6.If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the -square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
”εκΏδα 416 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
”εκΏδα 380 - If two angles of a triangle are equal, the sides opposite those angles are equal. AA . . A Given the triangle ABC, in which angle B equals angle C. To prove that AB = A C. Proof. 1. Construct the AA'B'C' congruent to A ABC, by making B'C' = BC, Zfi' = ZB, and Z C
”εκΏδα 494 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
”εκΏδα 138 - Generalising this operation, we have the common rule for finding the greatest common measure of any two numbers : — divide the greater by the less, and the divisor by the remainder continually till nothing remains, and the last divisor is the greatest common measure.
”εκΏδα 259 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
”εκΏδα 489 - But let one of them BD pass through the centre, and cut the other AC, which does not pass through the centre, at right angles, in the...
”εκΏδα 102 - COR. 1. Hence, because AD is the sum, and AC the difference of ' the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square ' of the sum of the lines." " COR. 2. From the demonstration it is manifest, that since the square ' of CD is quadruple of the square of CB, the square of any line is qua' druple of the square of half that line.