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 |
From inside the book
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Page 48
... rectangle AE is equal to the square ADFC , together with the rectangle CE . But the A rectangle AE is the rectangle ... twice the rectangle under the parts . A C K D G E F A B B On AB describe the square ACDB , and draw CB , and from O ...
... rectangle AE is equal to the square ADFC , together with the rectangle CE . But the A rectangle AE is the rectangle ... twice the rectangle under the parts . A C K D G E F A B B On AB describe the square ACDB , and draw CB , and from O ...
Page 49
... twice the rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO , and under AB and BO , ( by Prop . 2 , B. 2 , ) but the rectangle under AB and AO , is equal to the sum of the ...
... twice the rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO , and under AB and BO , ( by Prop . 2 , B. 2 , ) but the rectangle under AB and AO , is equal to the sum of the ...
Page 50
Euclides T W Herbert. FL be added , and the rectangle AG with the square FL , will be equal to the square CKMB . But ... twice the rectangle under CD and DB together with the square of DB ; add to both the square of CD , and the rectangle ...
Euclides T W Herbert. FL be added , and the rectangle AG with the square FL , will be equal to the square CKMB . But ... twice the rectangle under CD and DB together with the square of DB ; add to both the square of CD , and the rectangle ...
Page 51
... triangle , the rectangle under the sum and difference of the hypothenuse and one side , is equal to the square of the remaining side . COR . 4. The difference of the squares of two sides BA and AC , of any triangle BAC , is equal to twice ...
... triangle , the rectangle under the sum and difference of the hypothenuse and one side , is equal to the square of the remaining side . COR . 4. The difference of the squares of two sides BA and AC , of any triangle BAC , is equal to twice ...
Page 52
... twice the rectangle under BC and half of BF and FC , namely the distance of the point F from the middle point D of the side BC . B AEC B AED C COR . 5. - If from the vertex of an Isosceles triangle ABC , a right line BE , be drawn to AC ...
... twice the rectangle under BC and half of BF and FC , namely the distance of the point F from the middle point D of the side BC . B AEC B AED C COR . 5. - If from the vertex of an Isosceles triangle ABC , a right line BE , be drawn to AC ...
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.