Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 44
... circumference . A diameter of a circle is a straight line passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle are equal ; all the diameters are equal also , and each double of the ...
... circumference . A diameter of a circle is a straight line passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle are equal ; all the diameters are equal also , and each double of the ...
Seite 45
... circumference of a circle tn more than two points . For , if it is possible , let the straight line ADB meet the circumference CDE in three points , C , D , E. Take F , the center of the circle , and join FC , FD , FE . Then , because F ...
... circumference of a circle tn more than two points . For , if it is possible , let the straight line ADB meet the circumference CDE in three points , C , D , E. Take F , the center of the circle , and join FC , FD , FE . Then , because F ...
Seite 49
... circumference may be made to pass , and but one . B F . Let A , B , C be three points not in the same straight line ; they all lie in the circumference of the same circle . Join AB , AC , and bisect these lines by the perpendiculars DF ...
... circumference may be made to pass , and but one . B F . Let A , B , C be three points not in the same straight line ; they all lie in the circumference of the same circle . Join AB , AC , and bisect these lines by the perpendiculars DF ...
Seite 50
... circumference . Let ABG be a circle , the center of which is C , and the di- ameter AB ; and let AD be drawn from A perpendicular to AB ; AD will be a tangent to the circum- ference . In AD take any point E , and join CE ; then , since ...
... circumference . Let ABG be a circle , the center of which is C , and the di- ameter AB ; and let AD be drawn from A perpendicular to AB ; AD will be a tangent to the circum- ference . In AD take any point E , and join CE ; then , since ...
Seite 51
... circumference . The proposition admits of three cases : First . When the two parallels are se- cants , as AB , DE . Draw the radius CH perpendicular to AB ; it will also be per- pendicular to DE ( Prop . XXIII . , Cor . D 1 , B. I. ) ...
... circumference . The proposition admits of three cases : First . When the two parallels are se- cants , as AB , DE . Draw the radius CH perpendicular to AB ; it will also be per- pendicular to DE ( Prop . XXIII . , Cor . D 1 , B. I. ) ...
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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...