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 |
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Page 11
... greater than its part . 10. All right angles are equal 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 ...
... greater than its part . 10. All right angles are equal 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 ...
Page 13
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
Page 14
... greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two ...
... greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two ...
Page 15
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
Page 16
... greater than it ; which is impossi ble . E C F But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
... greater than it ; which is impossi ble . E C F But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
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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 Let the straight 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 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...
Page 54 - 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 82 - 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 31 - 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 11 - 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 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Page 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Page 298 - 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.