Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 6
... given to mathematics in our colleges is limited , and a variety of subjects demand attention , no attempt has been made to render this a complete record of all the known propositions of Geometry . On the contrary , nearly every thing ...
... given to mathematics in our colleges is limited , and a variety of subjects demand attention , no attempt has been made to render this a complete record of all the known propositions of Geometry . On the contrary , nearly every thing ...
Seite 7
... same Book , only the number of the Proposition is given ; but when the Proposition is found in a different Book , the number of the Book is also specified . ELEMENTS OF GEOMETRY . BOOK I. GENERAL PRINCIPLES . Definitions.
... same Book , only the number of the Proposition is given ; but when the Proposition is found in a different Book , the number of the Book is also specified . ELEMENTS OF GEOMETRY . BOOK I. GENERAL PRINCIPLES . Definitions.
Seite 23
... given point , and DE the given straight line ; from the point A only one perpendicular can be drawn to DE . D A CB E For , if possible , let there be drawn two perpendiculars AB , AC . Produce the line AB to F , making BF equal to AB ...
... given point , and DE the given straight line ; from the point A only one perpendicular can be drawn to DE . D A CB E For , if possible , let there be drawn two perpendiculars AB , AC . Produce the line AB to F , making BF equal to AB ...
Seite 24
... given straight line , and A any point without it . Draw AB per- pendicular to DE ; draw , also , theˆob- lique lines AC , AD , AE . Produce the line AB to F , making BF equal to AB , and join CF , DF . First . Because , in the triangles ...
... given straight line , and A any point without it . Draw AB per- pendicular to DE ; draw , also , theˆob- lique lines AC , AD , AE . Produce the line AB to F , making BF equal to AB , and join CF , DF . First . Because , in the triangles ...
Seite 25
... given straight line . PROPOSITION XVIII . THEOREM . If through the middle point of a straight line a perpendic- ular is drawn to this line : 1st . Each point in the perpendicular is equally distant from the two extremities of the line ...
... given straight line . PROPOSITION XVIII . THEOREM . If through the middle point of a straight line a perpendic- ular is drawn to this line : 1st . Each point in the perpendicular is equally distant from the two extremities of the line ...
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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
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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...