Euclid's Elements of GeometryBell & Daldy, 1872 - 261 páginas |
Dentro del libro
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Página 4
... double of the same , or of equals , are equal to one another . 7. Things which are halves of the same , or of equals , are equal to one another . 8. Magnitudes which coincide with one another are equal to one another . 9. The whole is ...
... double of the same , or of equals , are equal to one another . 7. Things which are halves of the same , or of equals , are equal to one another . 8. Magnitudes which coincide with one another are equal to one another . 9. The whole is ...
Página 29
... double of the triangle . For draw CD . The D E triangle BDC is equal to the triangle BAC ( by Prop . 37 ) , but BE is double of the triangle BDC ( by Prop 34 ) , therefore BE is also double of BAC . B C B E SCHOL . - Hence it appears ...
... double of the triangle . For draw CD . The D E triangle BDC is equal to the triangle BAC ( by Prop . 37 ) , but BE is double of the triangle BDC ( by Prop 34 ) , therefore BE is also double of BAC . B C B E SCHOL . - Hence it appears ...
Página 30
... double of the base DC of the parallelogram the triangle and the parallelogram will be equal . For draw AD , and since the triangles BAD , DAC are equal ( by Prop . 38 ) , BAC is double of the triangle DAC , but the parallelogram DF , is ...
... double of the base DC of the parallelogram the triangle and the parallelogram will be equal . For draw AD , and since the triangles BAD , DAC are equal ( by Prop . 38 ) , BAC is double of the triangle DAC , but the parallelogram DF , is ...
Página 34
... the angles A and X also equal , the triangles BAD , YXS are equal ( by Prop . 4 ) therefore the squares AC and XZ , which are double of them ( by Prop . 34 ) are equal . COR . 2.- If two squares AC and XZ be 34 FIRST BOOK .
... the angles A and X also equal , the triangles BAD , YXS are equal ( by Prop . 4 ) therefore the squares AC and XZ , which are double of them ( by Prop . 34 ) are equal . COR . 2.- If two squares AC and XZ be 34 FIRST BOOK .
Página 35
... double of the triangle ICA , because they are between the same parallels CI and AZ , and on the same base CI ( by Prop . 41 ) : and the paral- lelogram CE is double of the triangle BCF , because they are between the same parallels CF ...
... double of the triangle ICA , because they are between the same parallels CI and AZ , and on the same base CI ( by Prop . 41 ) : and the paral- lelogram CE is double of the triangle BCF , because they are between the same parallels CF ...
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.