Plane and Solid GeometryGinn, 1904 - 473 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα iii
... proof . As a further concession to the beginner , the reason for each statement in the early proofs is printed in small italics , immediately following the statement . This prevents the necessity of interrupting the logical train of ...
... proof . As a further concession to the beginner , the reason for each statement in the early proofs is printed in small italics , immediately following the statement . This prevents the necessity of interrupting the logical train of ...
Σελίδα 4
George Albert Wentworth. GENERAL TERMS . 18. A proof is a course of reasoning by which the truth or falsity of any statement is logically established . 19. An axiom is a statement admitted to be true without proof . 20. A theorem is a ...
George Albert Wentworth. GENERAL TERMS . 18. A proof is a course of reasoning by which the truth or falsity of any statement is logically established . 19. An axiom is a statement admitted to be true without proof . 20. A theorem is a ...
Σελίδα 15
... Proof . Place the ZACBZ DEF . = ACB on the DEF , so that the vertex C shall fall on the vertex E , and the side CB on the side EF . Then CA will fall on ED , ( because ACB and DEF are straight lines ) . :: ZACB = DEF . 847 § 60 Q. E. D. ...
... Proof . Place the ZACBZ DEF . = ACB on the DEF , so that the vertex C shall fall on the vertex E , and the side CB on the side EF . Then CA will fall on ED , ( because ACB and DEF are straight lines ) . :: ZACB = DEF . 847 § 60 Q. E. D. ...
Σελίδα 16
... Proof . AOB is a straight line . Hyp . .. ZAOB is a st . Z. § 66 But ZAOD + Z BOD = the st . ZAOB . Ax . 9 877 .. the AOD and BOD are supplementary . Q. E. D. 87. DEF . Adjacent angles that are supplements of each . other are called ...
... Proof . AOB is a straight line . Hyp . .. ZAOB is a st . Z. § 66 But ZAOD + Z BOD = the st . ZAOB . Ax . 9 877 .. the AOD and BOD are supplementary . Q. E. D. 87. DEF . Adjacent angles that are supplements of each . other are called ...
Σελίδα 18
... Proof . ZOCA and OCB are supplementary . ZOCA and ACP are supplementary , 886 886 ( if two adjacent angles have their exterior sides in a straight line , these angles are supplementary ) . .. OCB and ACP have the same supplement ...
... Proof . ZOCA and OCB are supplementary . ZOCA and ACP are supplementary , 886 886 ( if two adjacent angles have their exterior sides in a straight line , these angles are supplementary ) . .. OCB and ACP have the same supplement ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCDE AC² altitude apothem axis bisector bisects called centre chord circumference circumscribed coincide common construct curve denote diagonals diameter dihedral angles distance divided draw ellipse equidistant equilateral triangle equivalent face angles feet Find the area Find the locus frustum given circle given line given point given straight line given triangle greater Hence homologous homologous sides hypotenuse inches intersection lateral area lateral edges length limit middle point number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism prismatoid Proof prove Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon regular pyramid respectively right angle right circular right triangle secant segments similar slant height sphere spherical polygon spherical triangle square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangular prism trihedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 44 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 276 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.
Σελίδα 52 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 43 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.
Σελίδα 193 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Σελίδα 362 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 171 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Σελίδα 73 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Σελίδα 385 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.
Σελίδα 77 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.