Euclid's Elements of GeometryBell & Daldy, 1872 - 261 sider |
Inni boken
Resultat 1-5 av 32
Side 7
... triangle ABC , the triangles themselves agree , and are therefore equal ( by Ax . 8 ) . PROPOSITION V. THEOREM . In any isosceles triangle ( BAC ) the angles at the base ( ABC and ACB ) are equal : and if the equal sides be produced ...
... triangle ABC , the triangles themselves agree , and are therefore equal ( by Ax . 8 ) . PROPOSITION V. THEOREM . In any isosceles triangle ( BAC ) the angles at the base ( ABC and ACB ) are equal : and if the equal sides be produced ...
Side 8
... triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . D If not , let one of them BA be made greater than the other , cut off a right line BD equal to AC ( by Prop . 3 ) , and draw CD . Since , in the triangles ...
... triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . D If not , let one of them BA be made greater than the other , cut off a right line BD equal to AC ( by Prop . 3 ) , and draw CD . Since , in the triangles ...
Side 10
... ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 ) , draw DE , and upon it con- struct an equilateral triangle DFE ( by Prop . 1 ) . The right line joining the points A and F will bisect the given angle BAC ...
... ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 ) , draw DE , and upon it con- struct an equilateral triangle DFE ( by Prop . 1 ) . The right line joining the points A and F will bisect the given angle BAC ...
Side 15
... triangle are less than two right angles . COR . - If in any triangle , one angle be obtuse or right , the remaining angles will be acute , and if two angles be equal , they are acute . PROPOSITION XVIII . THEOREM . If in any triangle ( BAC ) ...
... triangle are less than two right angles . COR . - If in any triangle , one angle be obtuse or right , the remaining angles will be acute , and if two angles be equal , they are acute . PROPOSITION XVIII . THEOREM . If in any triangle ( BAC ) ...
Side 16
... triangle ABC , since the angle BCA is right , BAC will be acute ( by Cor . Prop . 17 ) , therefore BC is opposite the less angle , and therefore is less ( by Prop . 19 ) than BA , which is opposite the greater . PROPOSITION XX . THEOREM ...
... triangle ABC , since the angle BCA is right , BAC will be acute ( by Cor . Prop . 17 ) , therefore BC is opposite the less angle , and therefore is less ( by Prop . 19 ) than BA , which is opposite the greater . PROPOSITION XX . THEOREM ...
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.