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 39
... segments , AD and DC , of the side on which the perpendicular falls . For the square of the side AB is equal to the squares of AD and DB ( by Prop . 47 ) , and the square of BC is equal to the squares of BD and DC ( by Prop . 47 ) ...
... segments , AD and DC , of the side on which the perpendicular falls . For the square of the side AB is equal to the squares of AD and DB ( by Prop . 47 ) , and the square of BC is equal to the squares of BD and DC ( by Prop . 47 ) ...
Página 50
... segments of one , be equal to the rectangle under the segments of the other , the segments themselves shall be equal . A GEB C AFD + + If right lines be bisected , the thing is evident . But if they be not bisected , let there be AB and ...
... segments of one , be equal to the rectangle under the segments of the other , the segments themselves shall be equal . A GEB C AFD + + If right lines be bisected , the thing is evident . But if they be not bisected , let there be AB and ...
Página 51
... segments , BF and FC , of the side on which the perpendicular falls ( by Cor . 4. Prop.47 . B. 1 ) , and therefore when the perpendicular falls inside the triangle , to the rectangle under BC , the sum of these segments , and the ...
... segments , BF and FC , of the side on which the perpendicular falls ( by Cor . 4. Prop.47 . B. 1 ) , and therefore when the perpendicular falls inside the triangle , to the rectangle under BC , the sum of these segments , and the ...
Página 52
... segments of the base AE and EC , will be equal to the square of one of the other sides AB or BC . First , let BE be perpendicular to the base , and then ACwill be bisected ( by Cor . 1. Prop . 26. B. 1 ) , therefore the rectangle under ...
... segments of the base AE and EC , will be equal to the square of one of the other sides AB or BC . First , let BE be perpendicular to the base , and then ACwill be bisected ( by Cor . 1. Prop . 26. B. 1 ) , therefore the rectangle under ...
Página 53
... segment ( CB ) taken together , will be equal to twice the rectangle under the whole line ( AB ) and said segment ( CB ) together with the square of the other segment ( AC . ) On AB describe a square , and draw FB , from C draw CG ...
... segment ( CB ) taken together , will be equal to twice the rectangle under the whole line ( AB ) and said segment ( CB ) together with the square of the other segment ( AC . ) On AB describe a square , and draw FB , from C draw CG ...
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.