Euclid's Elements of GeometryBell & Daldy, 1872 - 261 páginas |
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Página 161
... contained in the second , as often as an equi - submultiple of the third is contained in the fourth . 6. Magnitudes which have the same ratio are called proportionals . 7. When a submultiple of the first is contained oftener in the ...
... contained in the second , as often as an equi - submultiple of the third is contained in the fourth . 6. Magnitudes which have the same ratio are called proportionals . 7. When a submultiple of the first is contained oftener in the ...
Página 164
... contained in the one , so often it is contained in the other . First let one of the given magnitudes , BC , be a multiple of A , and A is not oftener contained in the one than the ... contained oftener in DE than in BC ; 164 FIFTH BOOK .
... contained in the one , so often it is contained in the other . First let one of the given magnitudes , BC , be a multiple of A , and A is not oftener contained in the one than the ... contained oftener in DE than in BC ; 164 FIFTH BOOK .
Página 166
... often in the one as in the other , the given magnitudes will be equal . But , suppose one of them BC to be greater than the other , and let its excess be nC ; and assume a submultiple a of A , less than nC , and a is contained oftener ...
... often in the one as in the other , the given magnitudes will be equal . But , suppose one of them BC to be greater than the other , and let its excess be nC ; and assume a submultiple a of A , less than nC , and a is contained oftener ...
Página 167
... contained oftener in CD than B in EF ; take away B from EF as often as can be done , and nF remains less than B ; and take away A as often from CD , and since A is contained oftener in CD than B in EF , the remainder mD shall be either ...
... contained oftener in CD than B in EF ; take away B from EF as often as can be done , and nF remains less than B ; and take away A as often from CD , and since A is contained oftener in CD than B in EF , the remainder mD shall be either ...
Página 168
... often as can be done , and nD remains less than e ; and take it away as often from AB , and since it is contained oftener in AB than in CD ( by Hypoth . ) , the remainder mB shall be greater than e , or equal to it , and therefore ...
... often as can be done , and nD remains less than e ; and take it away as often from AB , and since it is contained oftener in AB than in CD ( by Hypoth . ) , the remainder mB shall be greater than e , or equal to it , and therefore ...
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.