Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 18
... 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 , & c . PROPOSITION VII . THEOREM . If two triangles have two angles , and the ...
... 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 , & c . PROPOSITION VII . THEOREM . If two triangles have two angles , and the ...
Seite 20
... angle ADB equal to ADC ; consequently , each of these an- gles is a right ... ACB ; then will the side AB be equal to the side AC . B D A For if AB is not ... ACB , DB is equal to AC , and BC is common to both triangles , also , by ...
... angle ADB equal to ADC ; consequently , each of these an- gles is a right ... ACB ; then will the side AB be equal to the side AC . B D A For if AB is not ... ACB , DB is equal to AC , and BC is common to both triangles , also , by ...
Seite 21
... angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it , or less . It is not equal , because then the side AB would be equal to the side AC ( Prop . XI . ) , which is con- trary to ...
... angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it , or less . It is not equal , because then the side AB would be equal to the side AC ( Prop . XI . ) , which is con- trary to ...
Seite 23
... angle A must be equal to the angle D. In the same manner , it may be proved that the angle B is equal to the angle E ... ACB is equal to the angle FCB ( Prop . VI . ) . But , since the angle ACB is , by supposition , a right angle , FCB ...
... angle A must be equal to the angle D. In the same manner , it may be proved that the angle B is equal to the angle E ... ACB is equal to the angle FCB ( Prop . VI . ) . But , since the angle ACB is , by supposition , a right angle , FCB ...
Seite 31
... angle ACD is equal to the two interior and opposite angles CAB , ABC ( Axiom 2 ) . To each of these equals add the angle ACB ; then will the sum of the two angles ACD , ACB be equal to the sum of the three angles ABČ , BCA , CAB . But ...
... angle ACD is equal to the two interior and opposite angles CAB , ABC ( Axiom 2 ) . To each of these equals add the angle ACB ; then will the sum of the two angles ACD , ACB be equal to the sum of the three angles ABČ , BCA , CAB . But ...
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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...