The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 sider |
Inni boken
Resultat 1-5 av 29
Side 19
... angle DEF , ACB to DFE , and BAC to EDF ; and the triangles ABC , DEF will be equal in area . . Proof . Let the ... BAC to take the position EGF , A falling at G inside the triangle DEF . Produce EG to meet DF in H. Now ( I. 2 ) , ED + ...
... angle DEF , ACB to DFE , and BAC to EDF ; and the triangles ABC , DEF will be equal in area . . Proof . Let the ... BAC to take the position EGF , A falling at G inside the triangle DEF . Produce EG to meet DF in H. Now ( I. 2 ) , ED + ...
Side 23
... angle of one , equal to two sides and the included angle of the other , each to each , the triangles will be equal ... BAC is equal to the angle EDF , AC will coincide with DF , and because AC is equal to DF , C AA CE will coincide with ...
... angle of one , equal to two sides and the included angle of the other , each to each , the triangles will be equal ... BAC is equal to the angle EDF , AC will coincide with DF , and because AC is equal to DF , C AA CE will coincide with ...
Side 24
... angle . Let BAC be a rectilineal angle . It is required to bisect it . Take any point D , in AB , and from AC cut off ( I. 1 ) AE equal to AD ; join DE , and on it describe ( I. 3 , Cor . ) the equilateral triangle DFE ; join AF . AF ...
... angle . Let BAC be a rectilineal angle . It is required to bisect it . Take any point D , in AB , and from AC cut off ( I. 1 ) AE equal to AD ; join DE , and on it describe ( I. 3 , Cor . ) the equilateral triangle DFE ; join AF . AF ...
Side 27
... angle A CB . Bisect ( I. 9 ) the angle BAC by AD , cutting BC in D. Then because in the triangles ADB , ADC , AB is equal ( Hyp . ) to AC , the angle BAD to the angle CAD , and AD common , the angles ABD , ACD ( I. 7 ) are equal ; and ...
... angle A CB . Bisect ( I. 9 ) the angle BAC by AD , cutting BC in D. Then because in the triangles ADB , ADC , AB is equal ( Hyp . ) to AC , the angle BAD to the angle CAD , and AD common , the angles ABD , ACD ( I. 7 ) are equal ; and ...
Side 30
... angle is greater than either of the opposite interior angles . Let the side BC of the triangle ABC be produced to D ; then will ACD be greater than either ABC or BAC ... angle AEB to the angle CEF ( I. 17 ) , there- fore ( I. 7 ) the angle ...
... angle is greater than either of the opposite interior angles . Let the side BC of the triangle ABC be produced to D ; then will ACD be greater than either ABC or BAC ... angle AEB to the angle CEF ( I. 17 ) , there- fore ( I. 7 ) the angle ...
Andre utgaver - Vis alle
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Uten tilgangsbegrensning - 1882 |
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 apothem bisect centre of similitude chord circle ABC circumference cone Corollary cylinder decagon describe diagonals diameter divided draw equal angles equiangular feet figure four right angles frustum given circle given straight line greater Hence inscribed interior angles intersect isosceles Let ABC line joining lune meet middle point multiplied number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism produced Prop proportional Proposition 12 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 triangle square surface symmetrical tangent Theorem Theorem.-If three sides triangle ABC vertex
Populære avsnitt
Side 53 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 81 - On a given straight line to describe a segment of a circle, containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Side 31 - Any two angles of a triangle are together less than two right angles.
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 rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 15 - 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 82 - To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle. Let ABC be the given circle, and D the given rectilineal angle ; it is required to cut off a segment from the circle ABC that shall contain an angle equal to the given angle D.
Side 62 - 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 166 - 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 15 - 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 120 - Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.