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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... Equation ; therefore , it is probable , that we had the word from the Arabic name of the Art , and not from the philosopher Geber . It appears that the Arabians received it from the Persians and Indians ; but the Persians seem to refer ...
... Equation ; therefore , it is probable , that we had the word from the Arabic name of the Art , and not from the philosopher Geber . It appears that the Arabians received it from the Persians and Indians ; but the Persians seem to refer ...
Page 1
... 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 BOOK . DEFINITIONS . 1. A point is that.
... 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 BOOK . DEFINITIONS . 1. A point is that.
Page 122
... + b4 a2 + 4a3b + 6a2b2 + 4ab3 + 64 Fourth power . The labour of multiplication with binomials , or com- pound 122 THIRD BOOK . Involution 39 29 Extraction of Roots, Equations of the First Degree, 99 99 Second Degree,
... + b4 a2 + 4a3b + 6a2b2 + 4ab3 + 64 Fourth power . The labour of multiplication with binomials , or com- pound 122 THIRD BOOK . Involution 39 29 Extraction of Roots, Equations of the First Degree, 99 99 Second Degree,
Page 128
... a2 + 2a = remainder . 3a4 a66a5 + 15a4 + 2a3 + 15a2 + 6a + 1 = 3rd power of the quotient . Any root out of any given quantity can be extracted by this Rule . EQUATIONS . It will be requisite here to briefly state 128 THIRD BOOK .
... a2 + 2a = remainder . 3a4 a66a5 + 15a4 + 2a3 + 15a2 + 6a + 1 = 3rd power of the quotient . Any root out of any given quantity can be extracted by this Rule . EQUATIONS . It will be requisite here to briefly state 128 THIRD BOOK .
Page 129
... equation is the equality of two quantities . The assemblage of quantities at the same side of the sign is called the member or side ; an equation has two sides . That which is at the left is called the first side , and the other is ...
... equation is the equality of two quantities . The assemblage of quantities at the same side of the sign is called the member or side ; an equation has two sides . That which is at the left is called the first side , and the other is ...
Common terms and phrases
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
Popular passages
Page 20 - If two triangles have two sides of the one equal to two sides of the...
Page 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 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.
Page 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.
Page 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.
Page 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.
Page 129 - In any proportion, the product of the means is equal to the product of the extremes.
Page 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.
Page 215 - ... are to one another in the duplicate ratio of their homologous sides.
Page 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.