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 41
Page 44
... ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallel- ograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the par- allelograms is double ( 34. 1 ) of the tri ...
... ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallel- ograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the par- allelograms is double ( 34. 1 ) of the tri ...
Page 45
... ABCD is equal to the parallelo- gram EBCF . Therefore , parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same paral- lels , are equal to one another . Let ABCD ...
... ABCD is equal to the parallelo- gram EBCF . Therefore , parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same paral- lels , are equal to one another . Let ABCD ...
Page 47
... ABCD and the triangle EBC be upon the same base BC and between the same par- A D E allels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is e- qual ( 37. 1. ) to the triangle EBC , be ...
... ABCD and the triangle EBC be upon the same base BC and between the same par- A D E allels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is e- qual ( 37. 1. ) to the triangle EBC , be ...
Page 48
... ABCD , and are there- fore called the complements : The E complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its diameter , the triangle ABC is equal ( 34. 1. ) to the triangle ADC : And because EKHA ...
... ABCD , and are there- fore called the complements : The E complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its diameter , the triangle ABC is equal ( 34. 1. ) to the triangle ADC : And because EKHA ...
Page 49
... ABCD be the given rectilineal figure , and E the given rec- tilineal angle . It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. Join DB , and describe ( 42. 1. ) the parallelogram FH equal to the ...
... ABCD be the given rectilineal figure , and E the given rec- tilineal angle . It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. Join DB , and describe ( 42. 1. ) the parallelogram FH equal to the ...
Other editions - View all
Common terms and phrases
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 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 magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB proportional 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 parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line AC THEOR third touches the circle triangle ABC wherefore
Popular passages
Page 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 41 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Page 36 - If two triangles have two sides of the one equal to two sides of the...
Page 33 - ANY two sides of a triangle are together greater than the third side.
Page 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 308 - 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.
Page 25 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Page 56 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 90 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.