Elements of Plane Geometry, Del 1Harper & Brothers, 1878 - 132 sider |
Inni boken
Resultat 1-5 av 28
Side 18
... common use begin with a theorem , and that theorem none of the easiest . In the present work the first proposition is a problem . But although this is the case the scholars should be compelled to draw accurately and neatly the following ...
... common use begin with a theorem , and that theorem none of the easiest . In the present work the first proposition is a problem . But although this is the case the scholars should be compelled to draw accurately and neatly the following ...
Side 23
... common to both . Hence the two triangles are every way equal ( Prop . IV . ) ; the angle CDB is equal to CEA , and CBD is equal to CAE , and the side DB is equal to the side EA . Again , in the two triangles ADB and BEA , the sides AD ...
... common to both . Hence the two triangles are every way equal ( Prop . IV . ) ; the angle CDB is equal to CEA , and CBD is equal to CAE , and the side DB is equal to the side EA . Again , in the two triangles ADB and BEA , the sides AD ...
Side 25
... common to both ; hence ( Prop . VII . ) the two triangles are every way equal , and the angle DAF is equal to the angle EAF . Scholium . By the same construction DAF and EAF may be divided into two equal parts ; and thus , by suc ...
... common to both ; hence ( Prop . VII . ) the two triangles are every way equal , and the angle DAF is equal to the angle EAF . Scholium . By the same construction DAF and EAF may be divided into two equal parts ; and thus , by suc ...
Side 26
... common ; hence they have three sides of the one equal to three sides of the other , each to each . Therefore the angle DCF ( Prop . VII . ) is equal to the angle ECF ; and , since these angles are equal , each is a right angle ( Def ...
... common ; hence they have three sides of the one equal to three sides of the other , each to each . Therefore the angle DCF ( Prop . VII . ) is equal to the angle ECF ; and , since these angles are equal , each is a right angle ( Def ...
Side 27
... common to both . Hence the two triangles are every way equal ( Prop . VII . ) , and the angle EHC is equal to the angle GHC ; and , since these angles are equal , each is a right angle ( Def . 10 ) . Therefore the line HC is ...
... common to both . Hence the two triangles are every way equal ( Prop . VII . ) , and the angle EHC is equal to the angle GHC ; and , since these angles are equal , each is a right angle ( Def . 10 ) . Therefore the line HC is ...
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Vanlige uttrykk og setninger
ABCD AC and BD AC and CB AC is equal ACEH adjacent angle allel alternate angles altitude angle ABC angle ACB angle BAC angle equal base centre chord circumference diagonal diameter draw equal angles equal const equal Prop equal to DF equiangular equilateral triangle exterior angle feet Find the area Geometry given line given point gles greater half the arc Hence the triangles hypothenuse included angle inscribed interior and opposite isosceles triangle Join the points Let ABC lines AC measured by half opposite angle parallelogram perpendicular point F polygon proportional PROPOSITION Prove quadrilateral radius rectangle rectangle contained Required the area rhombus right angles Prop right-angled triangle Scholium secant secant line segment side AC similar six right square tangent TEST EXAMPLES three sides trapezium triangle ABC
Populære avsnitt
Side 48 - 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 are equal in all respects.
Side 26 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Side 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 45 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Side 63 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Side 64 - 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 114 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Side 57 - If 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 two triangles will be equal.
Side 57 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 69 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.