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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...
No preview available - 2017
added addition already answering apply arithmetical begin breadth called centre circle circumference common compound consequently considered consists contain continued cube decimal definition denominator described determined difference direction distance divide dividend division divisor drawn equal evident exactly explained exponent expressed extend factors figures follows four fourth fraction geometrical give given greater half hand inclination instance integer kind length less letters logarithm magnitude mathematical matter means measure meet mind multiplier namely nature necessary notion obtained once operation opposite parallel particular performed plane portion position possible practical principle proportion quantity quotient ratio reason rectangle relation remaining represent respect result right angles root round scale side simple solid space square stand straight line subtraction surface taken thing third tion triangle truth understand understood units whole
Page 376 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.
Page 453 - 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.
Page 396 - 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.
Page 360 - 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
Page 100 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 474 - 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.
Page 136 - 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.
Page 243 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
Page 469 - 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...
Page 100 - 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.