Elements of Geometry and Conic Sections |
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Page 45
... curve line ACB must coincide exactly with the curve line ADB . For , if any part of the curve ACB were to fall either within or without the curve ADB , there would be points in one or the other unequally distant from the center , which ...
... curve line ACB must coincide exactly with the curve line ADB . For , if any part of the curve ACB were to fall either within or without the curve ADB , there would be points in one or the other unequally distant from the center , which ...
Page 46
... curve line AIDB will coincide entirely with the curve line EMHF ( Prop . I. ) . But the arc AID is , by hypothesis , equal to the arc EMH ; hence the point D will fall on the point H , and therefore the chord AD is equal to the chord EH ...
... curve line AIDB will coincide entirely with the curve line EMHF ( Prop . I. ) . But the arc AID is , by hypothesis , equal to the arc EMH ; hence the point D will fall on the point H , and therefore the chord AD is equal to the chord EH ...
Page 150
... curve ABD which bounds the sec- tion . The oblique lines CA , CB , CD are equal , because they are radii of the B sphere ; therefore they are equally distant from the perpen- dicular CE ( Prop . V. , Cor . , B. VII . ) . Hence all the ...
... curve ABD which bounds the sec- tion . The oblique lines CA , CB , CD are equal , because they are radii of the B sphere ; therefore they are equally distant from the perpen- dicular CE ( Prop . V. , Cor . , B. VII . ) . Hence all the ...
Page 176
... axis AD , may be found by subtracting that of the segment of one base generated by ABE , from that of the c segment of one base generated by ACD . B E CONIC SECTIONS . THERE are three curves whose properties are 176 GEOMETRY .
... axis AD , may be found by subtracting that of the segment of one base generated by ABE , from that of the c segment of one base generated by ACD . B E CONIC SECTIONS . THERE are three curves whose properties are 176 GEOMETRY .
Page 177
... curve perpen- dicular to the directrix . The vertex of the diameter is the point in which it cuts c the curve . A A Thus , through any point of the curve , as A , draw a line DE perpendicular to the directrix BC ; DE is a diameter of ...
... curve perpen- dicular to the directrix . The vertex of the diameter is the point in which it cuts c the curve . A A Thus , through any point of the curve , as A , draw a line DE perpendicular to the directrix BC ; DE is a diameter of ...
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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.