Euclid's Elements of GeometryBell & Daldy, 1872 - 261 páginas |
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Página 4
... meeting a right line , make the internal angles on the same side less than two right angles ; these two right lines , being produced , will meet one another on that side at which the angles are less than two right angles . PROPOSITION I ...
... meeting a right line , make the internal angles on the same side less than two right angles ; these two right lines , being produced , will meet one another on that side at which the angles are less than two right angles . PROPOSITION I ...
Página 13
... meeting another right line ( AB ) at the same point , and at different sides , make angles with it , which are equal to two right angles ; these right lines ( CB and BD ) will form one straight line . For if not , if it be possible ...
... meeting another right line ( AB ) at the same point , and at different sides , make angles with it , which are equal to two right angles ; these right lines ( CB and BD ) will form one straight line . For if not , if it be possible ...
Página 18
... meeting at the given point B , may be equal to the legs of FC and DC of the given angle C ( by Prop . 22. ) The angle B will be equal to the given angle C. For since the triangles DCF and EBA are equilateral , the angles C and B ...
... meeting at the given point B , may be equal to the legs of FC and DC of the given angle C ( by Prop . 22. ) The angle B will be equal to the given angle C. For since the triangles DCF and EBA are equilateral , the angles C and B ...
Página 21
... meeting , if it be possi- ble , in G , and the external angle AEF of the triangle EGF is greater than the internal angle EFG ( by c Prop . 16 ) , but it is equal ( by Hypoth . ) , which is absurd ; therefore the AB and CD do not meet ...
... meeting , if it be possi- ble , in G , and the external angle AEF of the triangle EGF is greater than the internal angle EFG ( by c Prop . 16 ) , but it is equal ( by Hypoth . ) , which is absurd ; therefore the AB and CD do not meet ...
Página 30
... meeting the right line AF , in F ; DF will be the parallelogram sought for . E For since EF is parallel to DC , ( by Construction , ) and CF to DE , ( by Construction , ) DEFC is a parallel- ogram , by Def . 30 ) ; it has likewise an ...
... meeting the right line AF , in F ; DF will be the parallelogram sought for . E For since EF is parallel to DC , ( by Construction , ) and CF to DE , ( by Construction , ) DEFC is a parallel- ogram , by Def . 30 ) ; it has likewise an ...
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.