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 100
Page
... 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 John Playfair. 量 POPULAR CLASSICAL AND SCHOOL BOOKS , PRINTED AND PUBLISHED BY.
... 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 John Playfair. 量 POPULAR CLASSICAL AND SCHOOL BOOKS , PRINTED AND PUBLISHED BY.
Page
... Plane and Spherical Trigonometry John Playfair. graphy , History , Literature , and Mythology of the Ancients . Re ... Plane Trigonometry , Mensuration , Surveying , Analytical Plane and Spherical Trigonometry , Analytical Geometry , the ...
... Plane and Spherical Trigonometry John Playfair. graphy , History , Literature , and Mythology of the Ancients . Re ... Plane Trigonometry , Mensuration , Surveying , Analytical Plane and Spherical Trigonometry , Analytical Geometry , the ...
Page 3
... Plane and Spherical Trigonometry John Playfair. 20. The sign of Addition is an erect cross ; thus A + B implies the sum of A and B , and is called A plus B. 21. Subtraction is denoted by a single line ; as A - B , which is read A minus B ...
... Plane and Spherical Trigonometry John Playfair. 20. The sign of Addition is an erect cross ; thus A + B implies the sum of A and B , and is called A plus B. 21. Subtraction is denoted by a single line ; as A - B , which is read A minus B ...
Page 6
... Plane and Spherical Trigonometry John Playfair. 15. Two lines are said to be parallel , when being situated in the same plane , they cannot meet , how far soever , either way , both of them be produced . 16. A plane figure , terminated ...
... Plane and Spherical Trigonometry John Playfair. 15. Two lines are said to be parallel , when being situated in the same plane , they cannot meet , how far soever , either way , both of them be produced . 16. A plane figure , terminated ...
Page 14
... Plane and Spherical Trigonometry John Playfair. rior angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC ...
... Plane and Spherical Trigonometry John Playfair. rior angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC ...
Other editions - View all
Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 46 - 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 39 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 47 - 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 on the line between the points of section, is equal to the square on half the line.
Page 25 - 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 5 - 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 75 - 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 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 294 - 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 52 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Page 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.