Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry).1846 |
Inni boken
Resultat 1-5 av 92
Side 7
... similarly demonstrated that the triangle AFB is equilateral . PROPOSITION II . PROBLEM . From a given point ( A ) to draw a right line equal to a given finite right line ( BC ) . From the given point A draw a right line AB to either ...
... similarly demonstrated that the triangle AFB is equilateral . PROPOSITION II . PROBLEM . From a given point ( A ) to draw a right line equal to a given finite right line ( BC ) . From the given point A draw a right line AB to either ...
Side 15
... similarly proved that no other line except BD is in the direction of it , therefore BD is a continua- tion of BC . PROPOSITION XV . THEOREM . If two right lines ( AB and CD ) cut one another , the vertical angles will be equal ( CEA to ...
... similarly proved that no other line except BD is in the direction of it , therefore BD is a continua- tion of BC . PROPOSITION XV . THEOREM . If two right lines ( AB and CD ) cut one another , the vertical angles will be equal ( CEA to ...
Side 16
... similarly proved , by producing AC , that the angle BCG is greater than the angle B , and therefore that ACD , which is equal to BCG ( by 15 Prop . ) is greater than B. COR . 1. - If from the point B , two right lines be drawn to the ...
... similarly proved , by producing AC , that the angle BCG is greater than the angle B , and therefore that ACD , which is equal to BCG ( by 15 Prop . ) is greater than B. COR . 1. - If from the point B , two right lines be drawn to the ...
Side 17
... similarly shown , by producing CB from the angle B , that the angle ABC together with A is less than two right angles . Therefore any two angles of a triangle are less than two right angles . COR . - If in any triangle , one angle be ...
... similarly shown , by producing CB from the angle B , that the angle ABC together with A is less than two right angles . Therefore any two angles of a triangle are less than two right angles . COR . - If in any triangle , one angle be ...
Side 19
... similarly greater than BAE ( by Prop . 16 ) , the angle BDC will be greater than BAE . SCHOL . The excess of the angle BDC above BAE is equal to the two angles ABD and ACD , as appears from Prop . 32 . PROPOSITION XXII . PROBLEM . Given ...
... similarly greater than BAE ( by Prop . 16 ) , the angle BDC will be greater than BAE . SCHOL . The excess of the angle BDC above BAE is equal to the two angles ABD and ACD , as appears from Prop . 32 . PROPOSITION XXII . PROBLEM . Given ...
Vanlige uttrykk og setninger
absurd AC and CB AC by Prop AC is equal angle ABC angle equal angles by Prop arch bisected centre circumference co-efficient Const construct contained oftener diameter divided divisor double equal angles equal by Constr equal by Hypoth equal by Prop equal right lines equal to AC equal to twice equi-multiples equi-submultiples equiangular equilateral external angle fore fraction given angle given circle given line given right line given triangle greater half a right inscribed less multiplied opposite parallel parallelogram perpendicular PROPOSITION quantities quotient ratio rectangle under AC remaining angles remaining side right angle right line AB right line AC SCHOL segment semicircle side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle twice the square whole
Populære avsnitt
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 209 - ... 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 218 - 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 114 - 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 90 - 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.
Side 129 - In any proportion, the product of the means is equal to the product of the extremes.
Side 163 - 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 215 - ... are to one another in the duplicate ratio of their homologous sides.
Side 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.