Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
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Página 16
... manner , it may be proved that no other can be in the same straight line with it but BD . Therefore , if at a point , & c . X PROPOSITION IV . THEOREM . Two straight lines , which have two points common , coincide with each other ...
... manner , it may be proved that no other can be in the same straight line with it but BD . Therefore , if at a point , & c . X PROPOSITION IV . THEOREM . Two straight lines , which have two points common , coincide with each other ...
Página 17
... 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 formed at the point of intersection , are ...
... 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 formed at the point of intersection , are ...
Página 23
... manner , it may be proved that the angle B is equal to the angle E , and the angle C to the angle F ; hence the two triangles are equal . Therefore , if two triangles , & c . Scholium . In equal triangles , the equal angles are oppo ...
... manner , it may be proved that the angle B is equal to the angle E , and the angle C to the angle F ; hence the two triangles are equal . Therefore , if two triangles , & c . Scholium . In equal triangles , the equal angles are oppo ...
Página 24
... than AC . For it has already been proved that AC is equal to CF ; and in the same manner it may be proved that AD is equal to DF . Now , by Prop . IX . , the sum of the two lines AC , CF is less than the sum of 24 GEOMETRY .
... than AC . For it has already been proved that AC is equal to CF ; and in the same manner it may be proved that AD is equal to DF . Now , by Prop . IX . , the sum of the two lines AC , CF is less than the sum of 24 GEOMETRY .
Página 52
... . VI . , B. I. ) , and the point B is in the circumference ABF . In the same manner , it may be shown to be in the circumference ABG , and hence the point B is in both circumferences . Therefore the two circumfe 52 GEOMETRY .
... . VI . , B. I. ) , and the point B is in the circumference ABF . In the same manner , it may be shown to be in the circumference ABG , and hence the point B is in both circumferences . Therefore the two circumfe 52 GEOMETRY .
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 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.
Página 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.
Página 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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.
Página 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 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.
Página 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.
Página 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.