Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 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 ...
Seite 12
... equal angles , are call- ed homologous sides or angles . 21. An axiom is a self - evident truth . 22. A theorem is a ... 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 a ... equal to the same thing are equal to each other . 2. If equals are added to equals , the wholes are equal . 3. If ...
Seite 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 ...
... 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 ...
Seite 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 ...
Seite 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 ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected CA² chord circle circumference cone contained convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given point given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum 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 quadrant radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium segment side AC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 27 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Seite 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 10 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another, each of them is a right angle; and the straight line which stands upon the other is called a perpendicular to it; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB.
Seite 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.
Seite 22 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 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.
Seite 41 - It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by...