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 10
... . Upon the same right line ( AB ) and on the same side of it , there cannot be constructed two triangles ( ACB , ADB ) whose conterminous sides ( AC and AD , BC and BD ) can be equal . For , if it be possible , let them be 10 FIRST BOOK .
... . Upon the same right line ( AB ) and on the same side of it , there cannot be constructed two triangles ( ACB , ADB ) whose conterminous sides ( AC and AD , BC and BD ) can be equal . For , if it be possible , let them be 10 FIRST BOOK .
Página 11
Euclides T W Herbert. For , if it be possible , let them be constructed , and first let the vertex of each c triangle fall without the other , and draw CD . Because , in the triangle CAD , the sides AD and AC are equal ( by Hypoth ...
Euclides T W Herbert. For , if it be possible , let them be constructed , and first let the vertex of each c triangle fall without the other , and draw CD . Because , in the triangle CAD , the sides AD and AC are equal ( by Hypoth ...
Página 15
... possible , let BE be in the same right line with CB , and the angles CBA E D and ABE will be equal to two right angles ( by Prop . 13 ) but CBA and ABD are equal to two right angles ( by Hypoth . ) ; therefore CBA and ABE are equal to ...
... possible , let BE be in the same right line with CB , and the angles CBA E D and ABE will be equal to two right angles ( by Prop . 13 ) but CBA and ABD are equal to two right angles ( by Hypoth . ) ; therefore CBA and ABE are equal to ...
Página 16
... possible , let BA , perpendicular to the right line ED fall at the side of the obtuse angle BCE , and the angle BAE will be less than the angle BCE ( by Def . 12 ) ; but BAE is greater than BCE ( by Prop . 16 ) which is absurd ...
... possible , let BA , perpendicular to the right line ED fall at the side of the obtuse angle BCE , and the angle BAE will be less than the angle BCE ( by Def . 12 ) ; but BAE is greater than BCE ( by Prop . 16 ) which is absurd ...
Página 22
... possible to be done , let one of them BA be greater than the other , and cut off the right line BG equal to the less DE , and draw CG . In the triangles GBC , EDF , the sides GB , BC are equal to the sides ED , DF ( by Constr . and ...
... possible to be done , let one of them BA be greater than the other , and cut off the right line BG equal to the less DE , and draw CG . In the triangles GBC , EDF , the sides GB , BC are equal to the sides ED , DF ( by Constr . and ...
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.