Euclid's Elements of GeometryBell & Daldy, 1872 - 261 páginas |
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Página 4
... whole is greater than its part . 10. Two right lines cannot enclose a space : 11. All right angles are equal to one another . 12. If two right lines , meeting a right line , make the internal angles on the same side less than two right ...
... whole is greater than its part . 10. Two right lines cannot enclose a space : 11. All right angles are equal to one another . 12. If two right lines , meeting a right line , make the internal angles on the same side less than two right ...
Página 8
... whole , which is absurd : therefore neither of the sides BA nor AC is greater than the other , therefore they are equal . Hence every equiangular triangle is also equilateral ; for whatsoever side is assumed for a base , the angles ...
... whole , which is absurd : therefore neither of the sides BA nor AC is greater than the other , therefore they are equal . Hence every equiangular triangle is also equilateral ; for whatsoever side is assumed for a base , the angles ...
Página 13
... whole , which is absurd . Therefore BE is not in the direct line with CB ; and it can be similarly proved that no other line except BD is in the direction of it , therefore BD is a continua- tion of BC . PROPOSITION XV . THEOREM . If ...
... whole , which is absurd . Therefore BE is not in the direct line with CB ; and it can be similarly proved that no other line except BD is in the direction of it , therefore BD is a continua- tion of BC . PROPOSITION XV . THEOREM . If ...
Página 24
... whole angle FBC is equal to the two angles A and C. The angle ABC with FBC is equal to two right angles ( by Prop . 13 ) , but FBC is equal to the two angles A and C ( by part 1st ) , therefore the angle ABC with the two angles A and C ...
... whole angle FBC is equal to the two angles A and C. The angle ABC with FBC is equal to two right angles ( by Prop . 13 ) , but FBC is equal to the two angles A and C ( by part 1st ) , therefore the angle ABC with the two angles A and C ...
Página 29
... whole , which is absurd ( by Ax . 1 ) . Therefore AF is not parallel to BC , and it may be similarly shown that no other line except AD is parallel to it , therefore AD is parallel to BC . PROPOSITION XL . THEOREM . Equal triangles ...
... whole , which is absurd ( by Ax . 1 ) . Therefore AF is not parallel to BC , and it may be similarly shown that no other line except AD is parallel to it , therefore AD is parallel to BC . PROPOSITION XL . THEOREM . Equal triangles ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2015 |
Términos y frases comunes
absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference CKMB co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle
Pasajes populares
Página 18 - If two triangles have two sides of the one equal to two sides of the...
Página 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 207 - ... 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 216 - 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 127 - In any proportion, the product of the means is equal to the product of the extremes.
Página 161 - 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 112 - 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 213 - ... are to one another in the duplicate ratio of their homologous sides.
Página 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Página 88 - 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.