Elements of Geometry and Conic SectionsHarper, 1849 - 226 Seiten |
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Seite 5
... contain , indeed , the essential part of an argument ; but the general student does not derive from them the high- est benefit which may accrue from the study of Geometry as an exercise in reasoning . While , then , in the following ...
... contain , indeed , the essential part of an argument ; but the general student does not derive from them the high- est benefit which may accrue from the study of Geometry as an exercise in reasoning . While , then , in the following ...
Seite 10
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . C B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ...
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . C B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ...
Seite 22
... contained by the sides of the other . Let ABC , DEF be two triangles having two sides of the one equal to Ꭺ two sides of the other , viz .: AB equal to DE , and AC to DF , but the base BC greater than the base EF ; then will the angle ...
... contained by the sides of the other . Let ABC , DEF be two triangles having two sides of the one equal to Ꭺ two sides of the other , viz .: AB equal to DE , and AC to DF , but the base BC greater than the base EF ; then will the angle ...
Seite 35
... contained an exact number of times in the preceding one . This last remainder will be the common measure of the proposed lines ; and regarding it as the meas- uring unit , we may easily find the values of the preceding remainders , and ...
... contained an exact number of times in the preceding one . This last remainder will be the common measure of the proposed lines ; and regarding it as the meas- uring unit , we may easily find the values of the preceding remainders , and ...
Seite 36
... contained an exact number of times in each of them . Let A and B represent two sur- faces , and let a square inch be the unit of measure . Now , if this measuring unit is contained B 15 times in A and 24 times in B , then the ratio of A ...
... contained an exact number of times in each of them . Let A and B represent two sur- faces , and let a square inch be the unit of measure . Now , if this measuring unit is contained B 15 times in A and 24 times in B , then the ratio of A ...
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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.