Elements of Geometry and Conic Sections |
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Page 37
... Proportion is an equality of ratios . Thus , if A has to B the same ratio that ... proportional quantities , the last is called a fourth proportional to the ... mean propor- tional between the other two . Def . 4. Two magnitudes are said ...
... Proportion is an equality of ratios . Thus , if A has to B the same ratio that ... proportional quantities , the last is called a fourth proportional to the ... mean propor- tional between the other two . Def . 4. Two magnitudes are said ...
Page 38
... means . It has been shown that the ratio of two magnitudes , wheth- er they are ... proportional quantities , so that A : B :: C : D ; then will AxD = BxC . For ... mean . Thus , if A : B :: B : C ; then , by the proposition , AXC = BxB ...
... means . It has been shown that the ratio of two magnitudes , wheth- er they are ... proportional quantities , so that A : B :: C : D ; then will AxD = BxC . For ... mean . Thus , if A : B :: B : C ; then , by the proposition , AXC = BxB ...
Page 74
... mean proportional between the segments of the hypothenuse . 3d . Each of the sides is a mean proportional between the hy- pothenuse and its segment adjacent to that side . Let ABC be a right - angled triangle , hav- ing the right angle ...
... mean proportional between the segments of the hypothenuse . 3d . Each of the sides is a mean proportional between the hy- pothenuse and its segment adjacent to that side . Let ABC be a right - angled triangle , hav- ing the right angle ...
Page 75
Elias Loomis. the perpendicular AD is a mean proportional between BD and DC , the two segments of the diameter ; that is , AD ' BDXDC . PROPOSITION XXIII . THEOREM . Two triangles , having an angle in the one equal to an angle in the ...
Elias Loomis. the perpendicular AD is a mean proportional between BD and DC , the two segments of the diameter ; that is , AD ' BDXDC . PROPOSITION XXIII . THEOREM . Two triangles , having an angle in the one equal to an angle in the ...
Page 79
... mean proportional be- tween the secant and its external segment . Cor . 2. If from a point without a circle , two secants be drawn , the rectangles contained by the whole secants and their external segments will be equivalent to each ...
... mean proportional be- tween the secant and its external segment . Cor . 2. If from a point without a circle , two secants be drawn , the rectangles contained by the whole secants and their external segments will be equivalent to each ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 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...
Page 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 148 - I.), that every section of a sphere made by a plane is a circle.