Elements of Plane and Solid GeometryGinn and Heath, 1877 - 398 σελίδες |
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Σελίδα 23
... and the same straight line . 6. Show that the two straight lines which bisect the two pairs of vertical angles are perpendicular to each other . PROPOSITION IX . THEOREM . 61. At a point in PERPENDICULAR AND OBLIQUE LINES . 23.
... and the same straight line . 6. Show that the two straight lines which bisect the two pairs of vertical angles are perpendicular to each other . PROPOSITION IX . THEOREM . 61. At a point in PERPENDICULAR AND OBLIQUE LINES . 23.
Σελίδα 47
... bisect the ZACB . In the ACE and BCE , AC BC , CE CE , = ZACE LBCE ; = ..AACE △ BCE , ( two are equal when two sides and the included respectively to two sides and the included ..ZA - LB , ( being homologous △ of equal △ ) . Hyp ...
... bisect the ZACB . In the ACE and BCE , AC BC , CE CE , = ZACE LBCE ; = ..AACE △ BCE , ( two are equal when two sides and the included respectively to two sides and the included ..ZA - LB , ( being homologous △ of equal △ ) . Hyp ...
Σελίδα 48
... bisects the base . C A E B Let the line CE bisect the ACB of the isosceles ДАСВ . We are to prove I. A ACE = ABCE ; II . line CE to AB ; III . A E = BE . I. In the ACE and BCE , AC = BC , Hyp . = CE CE , ZACE LBCE . = Iden . Cons ...
... bisects the base . C A E B Let the line CE bisect the ACB of the isosceles ДАСВ . We are to prove I. A ACE = ABCE ; II . line CE to AB ; III . A E = BE . I. In the ACE and BCE , AC = BC , Hyp . = CE CE , ZACE LBCE . = Iden . Cons ...
Σελίδα 50
... bisect EBC . Draw EF . In the AEBF and CBF EB = BC , = BF BF , = LEBF LCBF , .. the △ EBF and C B F are equal , Hyp . Iden . Cons . § 106 ( having two sides and the included of one equal respectively to two sides Now and the included ...
... bisect EBC . Draw EF . In the AEBF and CBF EB = BC , = BF BF , = LEBF LCBF , .. the △ EBF and C B F are equal , Hyp . Iden . Cons . § 106 ( having two sides and the included of one equal respectively to two sides Now and the included ...
Σελίδα 54
... bisects the △ B. Draw the Is OK , OP , and O H. In the rt . AOC K and OCP , OC = OC , = ZOCK ZOCP , ..A OCK = ДОСР , Iden . Cons . § 110 ( having the hypotenuse and an acute of the one equal respectively to the hypotenuse and an acute ...
... bisects the △ B. Draw the Is OK , OP , and O H. In the rt . AOC K and OCP , OC = OC , = ZOCK ZOCP , ..A OCK = ДОСР , Iden . Cons . § 110 ( having the hypotenuse and an acute of the one equal respectively to the hypotenuse and an acute ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCD altitude arc A B axis base and altitude bisect centre circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided Draw equal respectively equally distant equilateral equivalent figure frustum Geometry given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC limit line A B measured by arc middle point mutually equiangular number of sides opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 132 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 140 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 206 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 353 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 179 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 192 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 150 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.