Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
Inni boken
Resultat 1-5 av 31
Side 7
... fall on B , and the side DE on BA , and that the sides DF and BC may be at the same side ; then , because the sides DE and BA are equal , the point E must fall on A ; and , because the angles D and B are equal , the side DF must fall on ...
... fall on B , and the side DE on BA , and that the sides DF and BC may be at the same side ; then , because the sides DE and BA are equal , the point E must fall on A ; and , because the angles D and B are equal , the side DF must fall on ...
Side 9
... fall without the other , and draw CD . Because , in the triangle CAD , the sides AD and AC are equal ( by Hypoth ... fall without the other . CEE Now let the vertex D of either fall within the other ; and draw CD ; produce AC and AD to E ...
... fall without the other , and draw CD . Because , in the triangle CAD , the sides AD and AC are equal ( by Hypoth ... fall without the other . CEE Now let the vertex D of either fall within the other ; and draw CD ; produce AC and AD to E ...
Side 10
... fall on F ( by_Prop . 7 ) ; and the equal sides , AB and EF , CB and FD must agree , ( by Ax . 10 ) ; therefore , the angles B and F must coincide , and there- fore are equal ( by Ax . 8. ) A C E D SCHOL . It is manifest that the ...
... fall on F ( by_Prop . 7 ) ; and the equal sides , AB and EF , CB and FD must agree , ( by Ax . 10 ) ; therefore , the angles B and F must coincide , and there- fore are equal ( by Ax . 8. ) A C E D SCHOL . It is manifest that the ...
Side 14
... falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED , fall at the side ... fall at the side of the obtuse angle , therefore it falls at the side of the acute angle . COR . 2. Two ...
... falls at the side of the acute angle . For , if it be possible , let BA , perpendicular to the right line ED , fall at the side ... fall at the side of the obtuse angle , therefore it falls at the side of the acute angle . COR . 2. Two ...
Side 37
... fall on the opposite side , the diffe- rence of the squares of the sides AB and BC about that angle , will be equal to the difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . square For ...
... fall on the opposite side , the diffe- rence of the squares of the sides AB and BC about that angle , will be equal to the difference of the squares of the segments , AD and DC , of the side on which the perpendicular falls . square For ...
Andre utgaver - Vis alle
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Ingen forhåndsvisning tilgjengelig - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Ingen forhåndsvisning tilgjengelig - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 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.
Side 127 - In any proportion, the product of the means is equal to the product of the extremes.
Side 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.
Side 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.
Side 213 - ... are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.