Elements of Euclid Adapted to Modern Methods in GeometryWilliam Collins, Sons,, 1874 - 216 σελίδες |
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Αποτελέσματα 1 - 5 από τα 24.
Σελίδα 16
... difference between a postulate and an axiom , as between a problem and a theorem . A postulate is simply a problem so easy that there cannot be any set of directions laid down for doing it ; and that the mode of doing it must be known ...
... difference between a postulate and an axiom , as between a problem and a theorem . A postulate is simply a problem so easy that there cannot be any set of directions laid down for doing it ; and that the mode of doing it must be known ...
Σελίδα 31
... difference of any two sides of a triangle is less than the third side . For since AB and BC are greater than AC , if BC be taken from both , we shall have ( ax . 5. ) AB greater than the excess of AC above BC . PROP . XVI . - THEOREM ...
... difference of any two sides of a triangle is less than the third side . For since AB and BC are greater than AC , if BC be taken from both , we shall have ( ax . 5. ) AB greater than the excess of AC above BC . PROP . XVI . - THEOREM ...
Σελίδα 42
... difference between the reflex angle CDE and two right angles , that is , by the angle GDC . For , join EC ; then we have a convex figure ABCE . Now the exterior angles of the original figure ABCDE exceed those of the convex figure ABCE ...
... difference between the reflex angle CDE and two right angles , that is , by the angle GDC . For , join EC ; then we have a convex figure ABCE . Now the exterior angles of the original figure ABCDE exceed those of the convex figure ABCE ...
Σελίδα 56
... difference of the given squares . B Cor . 3.- -a . The difference of the squares of the sides of a triangle is equal to the difference of the squares of the seg- ments of the base made by a perpendicular . For the square of AB is equal ...
... difference of the given squares . B Cor . 3.- -a . The difference of the squares of the sides of a triangle is equal to the difference of the squares of the seg- ments of the base made by a perpendicular . For the square of AB is equal ...
Σελίδα 57
... difference of the squares on BD and DC . A A B C b . The second figure shews that the meaning of the term segment has to be extended ; it is not the line BC that is cut when the perpendicular falls outside the base , but its con ...
... difference of the squares on BD and DC . A A B C b . The second figure shews that the meaning of the term segment has to be extended ; it is not the line BC that is cut when the perpendicular falls outside the base , but its con ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1874 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC and CB altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference cloth coincide Const conv Cor.-Hence diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle Fcap GEOGRAPHY geometrical given circle given line given point given straight line greater half the perimeter Hence hypotenuse inscribed intersecting isosceles triangle less Let ABC LL.D meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure reflex angle remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent THEOREM triangle ABC twice the rectangle twice the square whole line
Δημοφιλή αποσπάσματα
Σελίδα 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 77 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Σελίδα 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.
Σελίδα 30 - Any two sides of a triangle are together greater than the third side.
Σελίδα 204 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.