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 |
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Αποτελέσματα 1 - 5 από τα 16.
Σελίδα 6
... 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. PROBLEM . On a given finite ...
... 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. PROBLEM . On a given finite ...
Σελίδα 15
... PROPOSITION XVI . THEOREM . If any side ( BC ) of a triangle be produced , the external angle ( ACD ) will be greater than either of the internal remote angles ( A or B. ) Bisect the side AC in E ( by Prop . FIRST BOOK . 15.
... PROPOSITION XVI . THEOREM . If any side ( BC ) of a triangle be produced , the external angle ( ACD ) will be greater than either of the internal remote angles ( A or B. ) Bisect the side AC in E ( by Prop . FIRST BOOK . 15.
Σελίδα 17
... internal angle ACB ( by Prop . 16 ) , therefore ABD is greater than ACB , and therefore ABC is greater than ACB . But ABC is opposite the greater side AC , and ACB is oppo- site the less side AB . PROPOSITION XIX . THEOREM . If in any ...
... internal angle ACB ( by Prop . 16 ) , therefore ABD is greater than ACB , and therefore ABC is greater than ACB . But ABC is opposite the greater side AC , and ACB is oppo- site the less side AB . PROPOSITION XIX . THEOREM . If in any ...
Σελίδα 19
... internal angle DEC , ( by Prop . 16 ) ; and DEC is 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 ...
... internal angle DEC , ( by Prop . 16 ) ; and DEC is 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 ...
Σελίδα 23
... internal angle EFG ( by c Prop . 16 ) , but it is equal ( by E B D G Hypoth . ) , which is absurd ; therefore the right lines . AB and CD do not meet towards B , D. It can be similarly demonstrated , that they do not meet at the FIRST ...
... internal angle EFG ( by c Prop . 16 ) , but it is equal ( by E B D G Hypoth . ) , which is absurd ; therefore the right lines . AB and CD do not meet towards B , D. It can be similarly demonstrated , that they do not meet at the FIRST ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 20 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 129 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 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.
Σελίδα 215 - ... are to one another in the duplicate ratio of their homologous sides.
Σελίδα 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.