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 |
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Page 5
... Magnitudes may be considered under three dimensions , -length , breadth , height or thickness . 2. In Geometry there are several general terms or principles ; such as , Definitions , Propositions , Axioms , Theorems , Problems , Lemmas ...
... Magnitudes may be considered under three dimensions , -length , breadth , height or thickness . 2. In Geometry there are several general terms or principles ; such as , Definitions , Propositions , Axioms , Theorems , Problems , Lemmas ...
Page 8
... magnitude . " ( See Notes . ) 2. A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the intersections " of one line with another are also points . " 3. " If two lines are such that they cannot ...
... magnitude . " ( See Notes . ) 2. A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the intersections " of one line with another are also points . " 3. " If two lines are such that they cannot ...
Page 11
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which ...
Page 106
... magnitude of any kind , it signifies that the " magnitude is multiplied by the number . Thus , 3A signifies three " times A ; mB , m times B , or a multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes ...
... magnitude of any kind , it signifies that the " magnitude is multiplied by the number . Thus , 3A signifies three " times A ; mB , m times B , or a multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes ...
Page 107
... Magnitudes are said to be of the same kind , when the less can be mul- tiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
... Magnitudes are said to be of the same kind , when the less can be mul- tiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
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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.