Elements of geometry, based on Euclid, books i-iii1876 - 119 sider |
Inni boken
Resultat 1-5 av 25
Side 11
... shown that BC is equal to BG . Therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another , therefore AL is equal to BC ( Ax . 1 ) . Therefore from the given point A a ...
... shown that BC is equal to BG . Therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another , therefore AL is equal to BC ( Ax . 1 ) . Therefore from the given point A a ...
Side 13
... shown . Proposition 5. - Theorem . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . = A DEF . ABC = Z DEF ...
... shown . Proposition 5. - Theorem . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . = A DEF . ABC = Z DEF ...
Side 15
... shown . COROLLARY . - Hence every equilateral triangle is also equiangular . Proposition 6. - Theorem . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall ...
... shown . COROLLARY . - Hence every equilateral triangle is also equiangular . Proposition 6. - Theorem . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall ...
Side 16
... shown to be greater than the angle BCD ( Dem . 5 ) . Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . B CASE II . - Let the vertex of one of the triangles fall within the other ...
... shown to be greater than the angle BCD ( Dem . 5 ) . Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . B CASE II . - Let the vertex of one of the triangles fall within the other ...
Side 17
... shown to be greater than the angle BCD . Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . Therefore , upon the same base , & c . Q. E , D. Proposition 8. - Theorem . If two triangles ...
... shown to be greater than the angle BCD . Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . Therefore , upon the same base , & c . Q. E , D. Proposition 8. - Theorem . If two triangles ...
Andre utgaver - Vis alle
Elements of Geometry, Based on Euclid, Bøker 1-3 Edward Atkins Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION describe diagonal diameter difference divided double draw drawn equal to CD exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.-Because proved Q. E. D. Proposition rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal
Populære avsnitt
Side 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Side 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Side 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 17 - If two triangles have two sides of the one equal to two sides of the...
Side 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Side 9 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 71 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Side 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 69 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.