The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1882 - 266 sider |
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Side 101
... altitudes . The altitude of a parallelogram is the perpen- Да dicular distance between either pair of parallel sides . 4. The homologous sides of similar rectilineal figures are those which are adjacent the equal angles ; in triangles 9 ...
... altitudes . The altitude of a parallelogram is the perpen- Да dicular distance between either pair of parallel sides . 4. The homologous sides of similar rectilineal figures are those which are adjacent the equal angles ; in triangles 9 ...
Side 102
... altitude are proportional to their bases . There are two cases : 1. Where the bases are commensur- able . 2. Where the bases are incommensurable . * 1. Let AB and CD be two rectangles having equal altitudes , AE and CF ; then AB CD ...
... altitude are proportional to their bases . There are two cases : 1. Where the bases are commensur- able . 2. Where the bases are incommensurable . * 1. Let AB and CD be two rectangles having equal altitudes , AE and CF ; then AB CD ...
Side 103
... altitude are propor- tional to their bases . For any parallelogram is equivalent to a rectangle having the same base and altitude ( I. 33 ) . Corollary 2. - Triangles of equal altitude are proportional to their bases . For a triangle is ...
... altitude are propor- tional to their bases . For any parallelogram is equivalent to a rectangle having the same base and altitude ( I. 33 ) . Corollary 2. - Triangles of equal altitude are proportional to their bases . For a triangle is ...
Side 104
... But ( V. 1 , Cor . 2 ) BDE : ADE :: BD : DA , the common altitude being the perpendicular drawn from E to AB . Similarly , CDE ADE :: CE : EA ; ... ( IV . 15 ) , BD : DA :: CE : EA . Next , let BD DA :: CE : EA ; 104 GEOMETRY . - BOOK V.
... But ( V. 1 , Cor . 2 ) BDE : ADE :: BD : DA , the common altitude being the perpendicular drawn from E to AB . Similarly , CDE ADE :: CE : EA ; ... ( IV . 15 ) , BD : DA :: CE : EA . Next , let BD DA :: CE : EA ; 104 GEOMETRY . - BOOK V.
Side 116
... altitude . For it is equal to a rectangle of the same base and altitude ( I. 33 ) . Corollary 2. - The area of a triangle is equal to one half the product of its base and altitude . For a triangle is one half a rectangle of the same ...
... altitude . For it is equal to a rectangle of the same base and altitude ( I. 33 ) . Corollary 2. - The area of a triangle is equal to one half the product of its base and altitude . For a triangle is one half a rectangle of the same ...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Uten tilgangsbegrensning - 1879 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Ingen forhåndsvisning tilgjengelig - 2016 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
A-BCD AB² ABCD altitude angle ABC angle ACB angle BAC base bisect centre of similitude chord circle ABC circumference cone Corollary cylinder decagon describe diagonals diameter divided draw equal angles equiangular feet figure find the volume four right angles frustum given circle given straight line greater Hence included angle inscribed interior angles intersection Let ABC meet middle point Multiply number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism Problem.-To Prop proportional Proposition 11 Proposition 13 pyramid quadrilateral radical axis radii radius rectangle contained regular polygon right angles Scholium segment semicircle similar similar triangles slant height solid solid angle sphere spherical angle spherical triangle square symmetrical tangent Theorem Theorem.-If triangle ABC vertex
Populære avsnitt
Side 56 - 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.
Side 77 - The angles in the same segment of a circle are equal to one another.
Side 81 - If a straight line touch a circle, and from the point of contact a...
Side 128 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the...
Side 17 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.
Side 110 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 64 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Side 164 - A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB: these together are less than four right angles. Let the planes...
Side 17 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.
Side 127 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...