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 v
... definition , except that of Euclid , has ever been given , from which the properties of proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the ...
... definition , except that of Euclid , has ever been given , from which the properties of proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the ...
Page vi
... definitions in the first book , and particularly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third ...
... definitions in the first book , and particularly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third ...
Page xii
... as he has not been careful in laying the foundation , he will never be successful in raising the superstructure . COLLEGE OF EDINBURGH , Dec. 1 , 1813 . 66 ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I. Xii PREFACE .
... as he has not been careful in laying the foundation , he will never be successful in raising the superstructure . COLLEGE OF EDINBURGH , Dec. 1 , 1813 . 66 ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I. Xii PREFACE .
Page 13
... DEFINITIONS . I. POINT is that which has position , but not magnitude . " * A ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the in- * tersections of one line with ...
... DEFINITIONS . I. POINT is that which has position , but not magnitude . " * A ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the in- * tersections of one line with ...
Page 18
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 39 - 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 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Page 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Page 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Page 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Page 51 - 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 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Page 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.