Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
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Página 11
... equal sides . 16. A right - angled triangle is one which has a right angle . The side opposite the right an- gle is ... equal , and its angles right angles . A rectangle is that which has all its angles right angles , but all its sides ...
... equal sides . 16. A right - angled triangle is one which has a right angle . The side opposite the right an- gle is ... equal , and its angles right angles . A rectangle is that which has all its angles right angles , but all its sides ...
Página 12
... equal angles , are call . ed homologous sides or angles . 21. An axiom is a self - evident truth . 22. A theorem is ... equal to the same thing are equal to each other .. 2. If equals are added to equals , the wholes are equal . 3. If ...
... equal angles , are call . ed homologous sides or angles . 21. An axiom is a self - evident truth . 22. A theorem is ... equal to the same thing are equal to each other .. 2. If equals are added to equals , the wholes are equal . 3. If ...
Página 14
... equal to the angle EGH . Take the four straight lines AC , CB , EG , GF , all equal to each other ; then will the line AB be equal to the line EF ( Axiom 2 ) . Let the line EF be applied to the line AB , so that the point E may be on A ...
... equal to the angle EGH . Take the four straight lines AC , CB , EG , GF , all equal to each other ; then will the line AB be equal to the line EF ( Axiom 2 ) . Let the line EF be applied to the line AB , so that the point E may be on A ...
Página 15
... equal to the sum of the three angles CBE , EBA , ABD ( Axiom 2 ) . Again , the angle DBE is equal to the sum of the two angles DBA , ABE . Add to each of these equals the angle EBC ; then will the sum of the two angles DBE , EBC be ...
... equal to the sum of the three angles CBE , EBA , ABD ( Axiom 2 ) . Again , the angle DBE is equal to the sum of the two angles DBA , ABE . Add to each of these equals the angle EBC ; then will the sum of the two angles DBE , EBC be ...
Página 16
... equal to two right angles ; therefore , the sum of the angles ABC , ABE is equal to the sum of the an- gles ABC , ABD . Take away the common angle ABC , and the remaining angle ABE , is equal ( Axiom 3 ) to the remain- ing angle ABD ...
... equal to two right angles ; therefore , the sum of the angles ABC , ABE is equal to the sum of the an- gles ABC , ABD . Take away the common angle ABC , and the remaining angle ABE , is equal ( Axiom 3 ) to the remain- ing angle ABD ...
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.