Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry).1846 |
Inni boken
Resultat 1-5 av 8
Side 63
... changed ; that is , make negative signs affir- mative , and affirmative signs negative ; and then incorporate them as in Addition . Ex . 1 . Ex . 2 . 5a 10d 2a 9d За d Ex . 3 . Ex . 4 . 8.x - - 8 : 2x 7x 6x 8z + 7x In Ex . 1 , we have ...
... changed ; that is , make negative signs affir- mative , and affirmative signs negative ; and then incorporate them as in Addition . Ex . 1 . Ex . 2 . 5a 10d 2a 9d За d Ex . 3 . Ex . 4 . 8.x - - 8 : 2x 7x 6x 8z + 7x In Ex . 1 , we have ...
Side 65
... changed whenever we remove it , thus , — ( a + b — c ) x = ax bx + cx ; and again , if we wish to place this in a parenthesis , it is also required that we should change the signs , thus , ax bx + cx becomes — ( a + b — c ) x . Ex . 15 ...
... changed whenever we remove it , thus , — ( a + b — c ) x = ax bx + cx ; and again , if we wish to place this in a parenthesis , it is also required that we should change the signs , thus , ax bx + cx becomes — ( a + b — c ) x . Ex . 15 ...
Side 108
... changed ) the signs of ac , and subtract them from the dividend ; the remainder will then be - ac , to which next bring down c3 , and proceed as before , and in all cases . - Ex . 2 264 a + b ) a1 — 3b4 ( a3 - a2b + ab2 - -63 a + b a1 + ...
... changed ) the signs of ac , and subtract them from the dividend ; the remainder will then be - ac , to which next bring down c3 , and proceed as before , and in all cases . - Ex . 2 264 a + b ) a1 — 3b4 ( a3 - a2b + ab2 - -63 a + b a1 + ...
Side 114
... changed . To reduce an improper fraction to a whole or mixed number . RULE . Divide the numerator by the denominator , as in Arithmetic . 1 . Qay — b ay b = - ay 2 . 10a2y + 3a3 262 = 10y + 3a - a2 262 a2 a2 + ab + b2 62 3 = a + b + a a ...
... changed . To reduce an improper fraction to a whole or mixed number . RULE . Divide the numerator by the denominator , as in Arithmetic . 1 . Qay — b ay b = - ay 2 . 10a2y + 3a3 262 = 10y + 3a - a2 262 a2 a2 + ab + b2 62 3 = a + b + a a ...
Side 120
... changed . 1. - Multiply by Ans . 862x 4bx 3 26 5 4bx 26 = 3 5 15 c + x DC 2. - Multiply by Ans ... x2 + cx cx 3. - Multiply a x2 2 2a a2 ax2 by Ans .... a DIVISION OF FRACTIONS . RULE . Divide the numerator of 120 THIRD BOOK .
... changed . 1. - Multiply by Ans . 862x 4bx 3 26 5 4bx 26 = 3 5 15 c + x DC 2. - Multiply by Ans ... x2 + cx cx 3. - Multiply a x2 2 2a a2 ax2 by Ans .... a DIVISION OF FRACTIONS . RULE . Divide the numerator of 120 THIRD BOOK .
Vanlige uttrykk og setninger
absurd AC and CB AC by Prop AC is equal angle ABC angle equal angles by Prop arch bisected centre circumference co-efficient Const construct contained oftener diameter divided divisor double equal angles equal by Constr equal by Hypoth equal by Prop equal right lines equal to AC equal to twice equi-multiples equi-submultiples equiangular equilateral external angle fore fraction given angle given circle given line given right line given triangle greater half a right inscribed less multiplied opposite parallel parallelogram perpendicular PROPOSITION quantities quotient ratio rectangle under AC remaining angles remaining side right angle right line AB right line AC SCHOL segment semicircle side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle twice the square whole
Populære avsnitt
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 209 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Side 218 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 114 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Side 90 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 129 - In any proportion, the product of the means is equal to the product of the extremes.
Side 163 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Side 215 - ... are to one another in the duplicate ratio of their homologous sides.
Side 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.