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 129
... proportional , the product of the means is equal to the product of the extremes ; in the proportion a : b :: c : d , a and d are the extremes , b and c the means . Wherefore , in order to prove the above numerically , they will stand ...
... proportional , the product of the means is equal to the product of the extremes ; in the proportion a : b :: c : d , a and d are the extremes , b and c the means . Wherefore , in order to prove the above numerically , they will stand ...
Página 163
... said to have a greater ratio to the fourth , than the first to the second . 8. Proportion is similitude of ratios . 9. And proportion consists in three terms , at least . L 10. When three magnitudes are proportional ( A to B.
... said to have a greater ratio to the fourth , than the first to the second . 8. Proportion is similitude of ratios . 9. And proportion consists in three terms , at least . L 10. When three magnitudes are proportional ( A to B.
Página 164
... proportional , the first is to the third as the second to the fourth ; as is shown in Prop . 33 , B. 5. Ex . gr . - A to B as C to Do , becomes A to C as B to Do. 15. By Inversion , when it is inferred that if four magnitudes be ...
... proportional , the first is to the third as the second to the fourth ; as is shown in Prop . 33 , B. 5. Ex . gr . - A to B as C to Do , becomes A to C as B to Do. 15. By Inversion , when it is inferred that if four magnitudes be ...
Página 165
... proportional , that the difference between the first and the second is to the second as the difference between the third and the fourth to the fourth ; as is proved in Cor . 2 , Prop . 25. Ex . gr . - A to B as C to D , becomes A B to B ...
... proportional , that the difference between the first and the second is to the second as the difference between the third and the fourth to the fourth ; as is proved in Cor . 2 , Prop . 25. Ex . gr . - A to B as C to D , becomes A B to B ...
Página 176
... proportional , the first to the second , as the third to the fourth ( A to CD , as B to EF ) , and there be assumed a submultiple ( a ) of the first , so that it be a submultiple of the second , an equi - submultiple ( b ) of the third ...
... proportional , the first to the second , as the third to the fourth ( A to CD , as B to EF ) , and there be assumed a submultiple ( a ) of the first , so that it be a submultiple of the second , an equi - submultiple ( b ) of the third ...
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.