Elements of Geometry and Conic Sections |
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Results 1-5 of 13
Page 16
... remaining angle ABE , is equal ( Axiom 3 ) to the remain- ing angle ABD , the less to the greater , which is impossible . Hence BE is not in the same straight line with BC ; and in like manner , it may be proved that no other can be in ...
... remaining angle ABE , is equal ( Axiom 3 ) to the remain- ing angle ABD , the less to the greater , which is impossible . Hence BE is not in the same straight line with BC ; and in like manner , it may be proved that no other can be in ...
Page 17
... remaining angle DEB ( Axiom 3 ) . In the same manner , it may be proved that the angle AED is equal to the angle CEB . Therefore , if two straight lines , & c . Cor . 1. Hence , if two straight lines cut one another , the four angles ...
... remaining angle DEB ( Axiom 3 ) . In the same manner , it may be proved that the angle AED is equal to the angle CEB . Therefore , if two straight lines , & c . Cor . 1. Hence , if two straight lines cut one another , the four angles ...
Page 18
Elias Loomis. and the remaining angles of the one , will coincide with the remaining angles of the other , and be equal to them , viz .: the angle ABC to the angle DEF , and the angle ACB to the an- gle DFE . Therefore , if two triangles ...
Elias Loomis. and the remaining angles of the one , will coincide with the remaining angles of the other , and be equal to them , viz .: the angle ABC to the angle DEF , and the angle ACB to the an- gle DFE . Therefore , if two triangles ...
Page 34
... remaining sides are equal , viz .: AE to ED , and CE to EB . Therefore , the diagonals of every parallelogram , & c . Čor . If the side AB is equal to AC , the triangles AEB , AEC have all the sides of the one equal to the corresponding ...
... remaining sides are equal , viz .: AE to ED , and CE to EB . Therefore , the diagonals of every parallelogram , & c . Čor . If the side AB is equal to AC , the triangles AEB , AEC have all the sides of the one equal to the corresponding ...
Page 57
... remaining side of the sec- ond is to the remaining side of the first . 5. In different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the center . Thus , if the angles A and D are equal ...
... remaining side of the sec- ond is to the remaining side of the first . 5. In different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the center . Thus , if the angles A and D are equal ...
Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Popular passages
Page 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 63 - 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.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 30 - 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 together equal to two right angles.