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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 19
... equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal . ΔΔΔ XXI . A scalene triangle , is that which has three unequal sides . XXII . A right angled triangle , is ...
... equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal . ΔΔΔ XXI . A scalene triangle , is that which has three unequal sides . XXII . A right angled triangle , is ...
Σελίδα 21
... one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. R1.
... one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. R1.
Σελίδα 22
... equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3. Pos- tulate ) the circle BCD ...
... equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3. Pos- tulate ) the circle BCD ...
Σελίδα 25
... equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub- tend , or are opposite to them , are also equal to one another . Let ABC be a triangle having the ...
... equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub- tend , or are opposite to them , are also equal to one another . Let ABC be a triangle having the ...
Σελίδα 27
... equilateral triangle DEF ; then join AF ; the straight line AF bi- sects the angle BAC . Because AD is equal to AE , and AF is common 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 bi- sects the angle BAC . Because AD is equal to AE , and AF is common 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 altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore