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 9
... fall on B , and the side DE on BA , and that the sides DF and BC may be at the same side ; then , because the sides DE and BA are equal , the point E must fall on A ; and , because the angles D and B are equal , the side DF must fall on ...
... fall on B , and the side DE on BA , and that the sides DF and BC may be at the same side ; then , because the sides DE and BA are equal , the point E must fall on A ; and , because the angles D and B are equal , the side DF must fall on ...
Página 11
... fall without the other . F Now let the vertex D of either fall within the other ; and draw CD produce AC and AD to E and F. Since in the triangle CAD , the sides AC and AD are equal , ( by Hypoth . ) the angles ECD and FDC are equal ...
... fall without the other . F Now let the vertex D of either fall within the other ; and draw CD produce AC and AD to E and F. Since in the triangle CAD , the sides AC and AD are equal , ( by Hypoth . ) the angles ECD and FDC are equal ...
Página 12
... fall on F ( by Prop . 7 ) ; and the equal sides , AB and EF , CB and FD must agree , ( by Ax . 10 ) ; therefore , the angles B and F must coincide , and there- fore are equal ( by Ax . 8. ) A с E SCHOL . It is manifest that the ...
... fall on F ( by Prop . 7 ) ; and the equal sides , AB and EF , CB and FD must agree , ( by Ax . 10 ) ; therefore , the angles B and F must coincide , and there- fore are equal ( by Ax . 8. ) A с E SCHOL . It is manifest that the ...
Página 16
... falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED fall at the side of ... fall at the side of the obtuse angle , therefore it falls at the side of the acute angle . COR . 2. Two ...
... falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED fall at the side of ... fall at the side of the obtuse angle , therefore it falls at the side of the acute angle . COR . 2. Two ...
Página 39
... fall on the opposite side , the diffe- rence of the squares of the sides AB and BC about that angle , will be equal to the difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . For the ...
... fall on the opposite side , the diffe- rence of the squares of the sides AB and BC about that angle , will be equal to the difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . For the ...
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.