Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical TrigonometryW. E. Dean, 1851 - 317 σελίδες |
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Σελίδα 10
... equilateral triangle is that which has three equal sides . 20. An isosceles triangle is that which has only two sides equal . ΔΔΔ 21. A scalene triangle is that which has three unequal sides . 22. A right angled triangle is that which ...
... equilateral triangle is that which has three equal sides . 20. An isosceles triangle is that which has only two sides equal . ΔΔΔ 21. A scalene triangle is that which has three unequal sides . 22. A right angled triangle is that which ...
Σελίδα 11
... are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 11.
... are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 11.
Σελίδα 12
... equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle ...
... equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle ...
Σελίδα 15
... equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ...
... equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ...
Σελίδα 17
... equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to ...
... equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore