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 Trigonometry |
From inside the book
Results 1-5 of 27
Page 27
... angles . PROP . XVI . THEOR . + If one side of a triangle be produced , the exterior an- gle is greater than either of the interior , and opposite an- gles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ...
... angles . PROP . XVI . THEOR . + If one side of a triangle be produced , the exterior an- gle is greater than either of the interior , and opposite an- gles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ...
Page 28
... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD , is greater ( 16.1 . ) than the interior and opposite angle ABC ; to each of these add the angle ACB ...
... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD , is greater ( 16.1 . ) than the interior and opposite angle ABC ; to each of these add the angle ACB ...
Page 30
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
Page 34
... angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the ... exterior angle BHA of the trian- gle AHC is equal to its interior and opposite angle BCA : which is im- possible ( 16.1 ...
... angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the ... exterior angle BHA of the trian- gle AHC is equal to its interior and opposite angle BCA : which is im- possible ( 16.1 ...
Page 35
... exterior angle AEF is greater ( 16. 1. ) than the interior and oppo- site angle EFG ; but it is also equal to it , which is impossible ; therefore , AB and CD being produced , do not meet towards B , D. In like manner it may be ...
... exterior angle AEF is greater ( 16. 1. ) than the interior and oppo- site angle EFG ; but it is also equal to it , which is impossible ; therefore , AB and CD being produced , do not meet towards B , D. In like manner it may be ...
Other editions - View all
Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar 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 meet multiple opposite angle parallel 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 125 - 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.
Page 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Page 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Page 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Page 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Page 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Page 51 - 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.
Page 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Page 55 - 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.