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 |
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Página 1
... Fractions " " " " ... ... 113 Involution 39 29 Extraction of Roots , Equations of the First Degree , 99 99 Second Degree , :: : 122 ... ... : 125 129 ... Numerical Proof of Euclid's Second Book , ... Algebraic 140 142 145 دو دو FIRST ...
... Fractions " " " " ... ... 113 Involution 39 29 Extraction of Roots , Equations of the First Degree , 99 99 Second Degree , :: : 122 ... ... : 125 129 ... Numerical Proof of Euclid's Second Book , ... Algebraic 140 142 145 دو دو FIRST ...
Página 107
... fraction , as xy RULE III . - a When the divisor and dividend consist of compound quantities , it will be necessary to arrange them accord- ing to the index of a similar quantity in each , so that the highest power may be first ...
... fraction , as xy RULE III . - a When the divisor and dividend consist of compound quantities , it will be necessary to arrange them accord- ing to the index of a similar quantity in each , so that the highest power may be first ...
Página 108
... fraction , because it is not divisible by it . EXAMPLES WITH ANSWERS . 1. - Divide a5 5a4b10a3b2 10a2b3 + 5ab1 -b5 by a22ab + b2 . -- Ans ... a3 3a2b3ab2 b3 . 2. - Divide 6x1 + 9x2 - 20x by 3x2 - 3x . 5.x Ans ... 2x2 + 2x + 5 - 3x2 3x 3 ...
... fraction , because it is not divisible by it . EXAMPLES WITH ANSWERS . 1. - Divide a5 5a4b10a3b2 10a2b3 + 5ab1 -b5 by a22ab + b2 . -- Ans ... a3 3a2b3ab2 b3 . 2. - Divide 6x1 + 9x2 - 20x by 3x2 - 3x . 5.x Ans ... 2x2 + 2x + 5 - 3x2 3x 3 ...
Página 112
... the Answers can be also written as follow : - - 2 1 Ex . 3 . a + b 5 = + b5 Ex . 6 . a 3 + a 5 = + an 1 Ex . 7. an - mb n X am b2n ALGEBRAIC FRACTIONS . The operations in Arithmetic and Algebraic Fractions 112 THIRD BOOK .
... the Answers can be also written as follow : - - 2 1 Ex . 3 . a + b 5 = + b5 Ex . 6 . a 3 + a 5 = + an 1 Ex . 7. an - mb n X am b2n ALGEBRAIC FRACTIONS . The operations in Arithmetic and Algebraic Fractions 112 THIRD BOOK .
Página 113
Euclides T W Herbert. ALGEBRAIC FRACTIONS . The operations in Arithmetic and Algebraic Fractions being nearly similar ... fraction , viz . , 4 + is a mixed number , and , in reducing it to an improper fraction , we must find how many 8ths ...
Euclides T W Herbert. ALGEBRAIC FRACTIONS . The operations in Arithmetic and Algebraic Fractions being nearly similar ... fraction , viz . , 4 + is a mixed number , and , in reducing it to an improper fraction , we must find how many 8ths ...
Términos y frases comunes
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
Pasajes populares
Página 20 - If two triangles have two sides of the one equal to two sides of the...
Página 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 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.
Página 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.
Página 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.
Página 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.
Página 129 - In any proportion, the product of the means is equal to the product of the extremes.
Página 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.
Página 215 - ... are to one another in the duplicate ratio of their homologous sides.
Página 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.