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 8
... coincide " in part , without coinciding altogether . " 66 4. A superficies is that which has only length and breadth . ' COR . The extremities of a superficies are lines ; and the intersections of one superficies with another are also ...
... coincide " in part , without coinciding altogether . " 66 4. A superficies is that which has only length and breadth . ' COR . The extremities of a superficies are lines ; and the intersections of one superficies with another are also ...
Page 11
... 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 intersect one ...
... 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 intersect one ...
Page 13
... coincide with the point E , because AB is equal to DE ; and AB * The three conclusions in this enunciation are more briefly expressed by saying , that the triangles are every way equal . coinciding with DE , AC shall coincide with DF ...
... coincide with the point E , because AB is equal to DE ; and AB * The three conclusions in this enunciation are more briefly expressed by saying , that the triangles are every way equal . coinciding with DE , AC shall coincide with DF ...
Page 14
... coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ...
... coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ...
Page 16
... coincide with the point F , because BC is equal to EF : therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if BA and CA do not coincide with ED and FD , but have a different situa- tion , as EG and FG ...
... coincide with the point F , because BC is equal to EF : therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if BA and CA do not coincide with ED and FD , but have a different situa- tion , as EG and FG ...
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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.