Elements of Geometry and Conic SectionsHarper, 1849 - 226 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 , the ob- lique lines AC , AD , AE . Produce the line AB to F , making BF equal to AB , and join CF , DF . D F F First . Because , in the ...
... given straight line , and A any point without it . Draw AB per- pendicular to DE ; draw , also , the ob- lique lines AC , AD , AE . Produce the line AB to F , making BF equal to AB , and join CF , DF . D F F First . Because , in the ...
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 . Every 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 . Every point in the perpendicular is equally distant from the two extremities of the line ...
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Häufige Begriffe und Wortgruppen
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained 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 greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin 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 Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
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Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 27 - VIf 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...
Seite 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
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 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 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.
Seite 15 - 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.
Seite 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.
Seite 148 - I.), that every section of a sphere made by a plane is a circle.