The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 13
... third side , B therefore AE + EB is greater than AB . Similarly CE + ED is greater than CD , therefore AE + EB ÷ CE + ED is greater than AB + CD . But AE + CE is equal to AC , and EB + ED is equal to DB , therefore AC + DB is greater ...
... third side , B therefore AE + EB is greater than AB . Similarly CE + ED is greater than CD , therefore AE + EB ÷ CE + ED is greater than AB + CD . But AE + CE is equal to AC , and EB + ED is equal to DB , therefore AC + DB is greater ...
Σελίδα 25
... third side . 3. If lines be drawn ( as in the last example ) from each of the vertices of the triangle in succession , prove that the perimeter of the triangle will be greater than the sum of these lines , and less than double that sum ...
... third side . 3. If lines be drawn ( as in the last example ) from each of the vertices of the triangle in succession , prove that the perimeter of the triangle will be greater than the sum of these lines , and less than double that sum ...
Σελίδα 38
... third straight line they cannot meet one another ; or , in other words , through any one point no more than one straight line can be drawn parallel to the same straight line PROPOSITION 18 . If a straight line , cutting two other ...
... third straight line they cannot meet one another ; or , in other words , through any one point no more than one straight line can be drawn parallel to the same straight line PROPOSITION 18 . If a straight line , cutting two other ...
Σελίδα 45
... third angle of the first triangle will be equal to the third angle of the second . - Note . We have seen in Props . 5 , 6 , and 7 , that two triangles are equal in all their parts when— Ist . Two sides and the included angle of the one ...
... third angle of the first triangle will be equal to the third angle of the second . - Note . We have seen in Props . 5 , 6 , and 7 , that two triangles are equal in all their parts when— Ist . Two sides and the included angle of the one ...
Σελίδα 56
... third of ABC . 4. On the side AB of the triangle ABC take AD equal to AC , produce BA and take AE equal to AC , then join the angle C to the points D and E. Prove that the angle at E is half BAC and that DCE is a right angle . 5. Prove ...
... third of ABC . 4. On the side AB of the triangle ABC take AD equal to AC , produce BA and take AE equal to AC , then join the angle C to the points D and E. Prove that the angle at E is half BAC and that DCE is a right angle . 5. Prove ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC and DEF ABCD adjacent angles angle ABC angle ACB angle BAC BC is equal centre circumference coincide common measure construction Corollary diameter dicular dihedral angle distance divided equal angles equal to AC equidistant exterior angle figure four right angles given angle given circle given plane given point given ratio given straight line greater homologous inscribed intersecting straight lines length less Let ABC line of intersection locus magnitudes meet the circle middle point multiple number of sides opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 13 Prove radii radius rectangle regular polygon respectively equal rhombus right angles segments side BC similar triangles Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Δημοφιλή αποσπάσματα
Σελίδα 15 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Σελίδα 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Σελίδα 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Σελίδα 204 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 14 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 12 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 161 - Ir there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words