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 47
Side 5
... Parallel right lines , are those which are in the same plane , and although produced , never meet . 29. A quadrilateral figure , is a rectilineal figure which is contained by four right lines . 30. A parallelogram , is a quadrilateral ...
... Parallel right lines , are those which are in the same plane , and although produced , never meet . 29. A quadrilateral figure , is a rectilineal figure which is contained by four right lines . 30. A parallelogram , is a quadrilateral ...
Side 23
... parallel . Α For suppose them not to be parallel , but 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 E B D G ...
... parallel . Α For suppose them not to be parallel , but 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 E B D G ...
Side 24
... parallel ( by Def . 28. ) PROPOSITION XXVIII . THEOREM . If a right line ( EF ) cutting two right lines ( AB and CD ... parallel . First , let EGA and GHC be equal ; and because EGA is equal to RGH ( by Prop . A 15 ) , GHC and RGH will ...
... parallel ( by Def . 28. ) PROPOSITION XXVIII . THEOREM . If a right line ( EF ) cutting two right lines ( AB and CD ... parallel . First , let EGA and GHC be equal ; and because EGA is equal to RGH ( by Prop . A 15 ) , GHC and RGH will ...
Side 25
... parallel ( by Hypoth . ) , and therefore cannot meet , which is absurd ; therefore neither of the angles AGH and GHD ... parallel to the same right line ( DN ) , they will be parallel to one another . G A L B Ο -N D. For let the right ...
... parallel ( by Hypoth . ) , and therefore cannot meet , which is absurd ; therefore neither of the angles AGH and GHD ... parallel to the same right line ( DN ) , they will be parallel to one another . G A L B Ο -N D. For let the right ...
Side 26
... parallel ( by Prop . 28. ) PROPOSITION XXXI . PROBLEM . To draw a right line parallel to a given right line , ( AB ) through a given point ( C ) without it . D Draw the right line CF , cutting the given line AB . At the point C , and ...
... parallel ( by Prop . 28. ) PROPOSITION XXXI . PROBLEM . To draw a right line parallel to a given right line , ( AB ) through a given point ( C ) without it . D Draw the right line CF , cutting the given line AB . At the point C , and ...
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.