The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |
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Page 84
... circles ABC , ADE touch one another ex- ternally at the point A ; and let F be the centre of the circle ABC , and G the centre of the circle ADE : the straight line which joins the points F , G , shall pass through the point A. For , if ...
... circles ABC , ADE touch one another ex- ternally at the point A ; and let F be the centre of the circle ABC , and G the centre of the circle ADE : the straight line which joins the points F , G , shall pass through the point A. For , if ...
Page 90
... circle from the extremity of it , touches the circle ; [ III . Def.2 . and that it touches the circle at one point only , because if it did meet the circle at two points it would fall within it . [ III . 2 . Also it is evident , that ...
... circle from the extremity of it , touches the circle ; [ III . Def.2 . and that it touches the circle at one point only , because if it did meet the circle at two points it would fall within it . [ III . 2 . Also it is evident , that ...
Page 91
... circle , from the extremity of it , touches the circle ; [ III . 16 , Corollary . therefore AB touches the circle . And AB is drawn from the given point A. Q.E.F. But if the given point be in the circumference of the circle , as the ...
... circle , from the extremity of it , touches the circle ; [ III . 16 , Corollary . therefore AB touches the circle . And AB is drawn from the given point A. Q.E.F. But if the given point be in the circumference of the circle , as the ...
Page 92
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of ... touches the circle ABC , and FC is drawn from the centre to the point of contact , FC B is perpendicular to DE ...
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of ... touches the circle ABC , and FC is drawn from the centre to the point of contact , FC B is perpendicular to DE ...
Page 104
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle ...
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle ...
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Common terms and phrases
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Popular passages
Page 262 - 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.
Page 71 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Page 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Page 182 - 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 8 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Page 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Page 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 60 - 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. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Page 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Page 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.