The New Practical Builder and Workman's Companion, Containing a Full Display and Elucidation of the Most Recent and Skilful Methods Pursued by Architects and Artificers ... Including, Also, New Treatises on Geometry ..., a Summary of the Art of Building ..., an Extensive Glossary of the Technical Terms ..., and The Theory and Practice of the Five Orders, as Employed in Decorative ArchitectureThomas Kelly, 1823 - 596 páginas |
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Página 21
... Hence every equilateral triangle is also equiangular . 62. COROLLARY 2. — A straight line drawn from the vertex of an isosceles triangle to the middle of the base will bisect the vertical angle , and be perpendicular to the base ...
... Hence every equilateral triangle is also equiangular . 62. COROLLARY 2. — A straight line drawn from the vertex of an isosceles triangle to the middle of the base will bisect the vertical angle , and be perpendicular to the base ...
Página 24
... hence the triangle ABC is equal to the triangle DEF . THEOREM 17 . 68. Two straight lines perpendicular to a third are parallel . For , if the straight lines AC , BD , be not parallel , they will meet on one side or the other of the ...
... hence the triangle ABC is equal to the triangle DEF . THEOREM 17 . 68. Two straight lines perpendicular to a third are parallel . For , if the straight lines AC , BD , be not parallel , they will meet on one side or the other of the ...
Página 27
... hence , FB and EK must be on opposite sides of EA ; and , therefore , can never meet . The truth of this proposition is assumed as an axiom in the Elements of Euclid , and made the foundation of parallel lines . THEOREM 25 . 77. Two ...
... hence , FB and EK must be on opposite sides of EA ; and , therefore , can never meet . The truth of this proposition is assumed as an axiom in the Elements of Euclid , and made the foundation of parallel lines . THEOREM 25 . 77. Two ...
Página 28
... Hence the outward angle is equal to the sum of the inward opposite angles . Again , because the angle BAD is equal to the sum of the angles B and C , add to each the angle BAC , and the sum of the two angles BAC , BAD , will be equal to ...
... Hence the outward angle is equal to the sum of the inward opposite angles . Again , because the angle BAD is equal to the sum of the angles B and C , add to each the angle BAC , and the sum of the two angles BAC , BAD , will be equal to ...
Página 29
... hence the side AD is parallel to BC ( theorem 19 ) . For the like reason AB is parallel to CD : therefore the quadrilateral , ABCD , is a parallelogram . THEOREM 30 . 87. A straight line , BD , drawn perpendicular to the extremity of a ...
... hence the side AD is parallel to BC ( theorem 19 ) . For the like reason AB is parallel to CD : therefore the quadrilateral , ABCD , is a parallelogram . THEOREM 30 . 87. A straight line , BD , drawn perpendicular to the extremity of a ...
Términos y frases comunes
ABCD abscissa adjacent angles altitude angle ABD annular vault axes axis major base bisect called centre chord circle circumference cone conic section conjugate contains COROLLARY 1.-Hence cutting cylinder describe a semi-circle describe an arc diameter distance divide draw a curve draw lines draw the lines edge ellipse Engraved equal angles equal to DF equation equiangular figure GEOMETRY given straight line greater groin homologous sides hyperbola intersection join joist latus rectum less Let ABC line of section meet multiplying Nicholson opposite sides ordinate parallel to BC parallelogram perpendicular PLATE points of section polygon PROBLEM produced proportionals quantity radius rectangle regular polygon ribs right angles roof segment similar triangles square straight edge subtracted surface Symns tangent THEOREM timber transverse axis triangle ABC vault vertex wherefore
Pasajes populares
Página 27 - 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.
Página 20 - 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'.
Página 51 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Página 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal.
Página 15 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 28 - ... angles of another, the third angles will also be equal, and the two triangles will be mutually equiangular. Cor.
Página 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página 80 - The sine of an arc is a straight line drawn from one extremity of the arc perpendicular to the radius passing through the other extremity. The tangent of an arc is a straight line touching the arc at one extremity, and limited by the radius produced through the other extremity.
Página 28 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Página 22 - The perpendicular is the shortest line that can be drawn from a point to a straight line.