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 Sperical Trigonometry |
From inside the book
Results 1-5 of 87
Page 4
... propositions of the fifth Book than those of any other of the Elements . In the second Book , also , some algebraic signs have been introduced , for the sake of representing more readily the addition and subtraction of the rectangles on ...
... propositions of the fifth Book than those of any other of the Elements . In the second Book , also , some algebraic signs have been introduced , for the sake of representing more readily the addition and subtraction of the rectangles on ...
Page 5
... proposition , requiring no formal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater than a part of it ; or , the whole is equal to all its parts ...
... proposition , requiring no formal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater than a part of it ; or , the whole is equal to all its parts ...
Page 6
... proposition to be true , by proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions ...
... proposition to be true , by proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions ...
Page 7
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
Page 11
... 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.
... 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.
Other editions - View all
Common terms and phrases
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 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
Popular passages
Page 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 68 - THE angles in the same segment of a circle are equal to one another...
Page 23 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Page 74 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 78 - 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.
Page 9 - 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 75 - If a straight line touch a circle, and from the point of contact a...
Page 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Page 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.