The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1882 - 266 Seiten |
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Seite 13
... triangle , an equilateral triangle is one which has three equal sides . 17. An isosceles triang1e is one which has two equal sides . 18. A scalene triangle is one which has three unequal sides . 19. Considering only the angles of a ...
... triangle , an equilateral triangle is one which has three equal sides . 17. An isosceles triang1e is one which has two equal sides . 18. A scalene triangle is one which has three unequal sides . 19. Considering only the angles of a ...
Seite 17
... triangle are together greater than the third side . Restatement . Let ABC be a triangle ; any two sides are together greater than the third . Proof . Because ( Ax . 12 ) the shortest distance between two points is B C the straight line ...
... triangle are together greater than the third side . Restatement . Let ABC be a triangle ; any two sides are together greater than the third . Proof . Because ( Ax . 12 ) the shortest distance between two points is B C the straight line ...
Seite 18
... triangle GDF is the required triangle . Proof . Because DG is a radius of the circle GHK , it is equal ( Def . 30 ) to B ; and because FG is a radius of GKL , it is equal to C ; and DF was made equal to A ; therefore GDF is a triangle ...
... triangle GDF is the required triangle . Proof . Because DG is a radius of the circle GHK , it is equal ( Def . 30 ) to B ; and because FG is a radius of GKL , it is equal to C ; and DF was made equal to A ; therefore GDF is a triangle ...
Seite 19
... triangles which have BA , AC , and the angle A , equal to ED , DF and the angle D , each to each ; then will the triangles be equal in all their parts . + Let the triangle ABC be applied * to the triangle DEF , so that A shall be on D ...
... triangles which have BA , AC , and the angle A , equal to ED , DF and the angle D , each to each ; then will the triangles be equal in all their parts . + Let the triangle ABC be applied * to the triangle DEF , so that A shall be on D ...
Seite 20
... triangles which have the two angles ABC , ACB , and the side BC , respectively equal to DEF , DFE , and the side EF . The triangles will be equal in all their parts . A D Apply the triangle ABC to the triangle DEF , so that B will be on ...
... triangles which have the two angles ABC , ACB , and the side BC , respectively equal to DEF , DFE , and the side EF . The triangles will be equal in all their parts . A D Apply the triangle ABC to the triangle DEF , so that B will be on ...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Keine Leseprobe verfügbar - 2016 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 77 - The angles in the same segment of a circle are equal to one another.
Seite 81 - If a straight line touch a circle, and from the point of contact a...
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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...