Elements of Geometry;: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical Trigonometry |
From inside the book
Results 1-5 of 19
Page 142
... therefore A is equal to B. Next , let C : A :: C : B , A = B . For by inverfion b , A : C : B : C ; and therefore by the first case , A = B . b A. 5 . PROP . Book V. PROP . X. THEO R. THAT magnitude which 1 142 ELEMENTS 1 ...
... therefore A is equal to B. Next , let C : A :: C : B , A = B . For by inverfion b , A : C : B : C ; and therefore by the first case , A = B . b A. 5 . PROP . Book V. PROP . X. THEO R. THAT magnitude which 1 142 ELEMENTS 1 ...
Page 150
... case , fince C > A , F > D , that is , D < F . There- fore , & c . Q. E. D. a 4. 5 . b 20. 5 . PROP . XXII . THEOR . F there be any number of magnitudes , and as many others , which , taken two and two in order , have the fame ratio ...
... case , fince C > A , F > D , that is , D < F . There- fore , & c . Q. E. D. a 4. 5 . b 20. 5 . PROP . XXII . THEOR . F there be any number of magnitudes , and as many others , which , taken two and two in order , have the fame ratio ...
Page 152
... case A : C : : E : G. But C : D :: G : H , therefore again , by the first case , ADE H. In the fame manner may the demonstration be extended to any number of magnitudes . Therefore , & c . Q. E. D. : a 22.5 . b 18. 5 . IT PROP . XXIV ...
... case A : C : : E : G. But C : D :: G : H , therefore again , by the first case , ADE H. In the fame manner may the demonstration be extended to any number of magnitudes . Therefore , & c . Q. E. D. : a 22.5 . b 18. 5 . IT PROP . XXIV ...
Page 166
... case . PROP . VIII . THEOR . Na right angled triangle , if a perpendicular be IN drawn from the right angle to the base ; the tri- angles on each fide of it are fimilar to the whole triangle , and to one another . Let ABC be a right ...
... case . PROP . VIII . THEOR . Na right angled triangle , if a perpendicular be IN drawn from the right angle to the base ; the tri- angles on each fide of it are fimilar to the whole triangle , and to one another . Let ABC be a right ...
Page 234
... case , the folid AE is equal to the folid CF ; but the folid AE is equal to the folid SE , as was demonftrated ; therefore the folid SE is equal to the fo- lid CF. Cafe 2. If the infifting ftraight lines AG , HK , BE , LM ; CN , RS , DF ...
... case , the folid AE is equal to the folid CF ; but the folid AE is equal to the folid SE , as was demonftrated ; therefore the folid SE is equal to the fo- lid CF. Cafe 2. If the infifting ftraight lines AG , HK , BE , LM ; CN , RS , DF ...
Other editions - View all
Common terms and phrases
ABCD adjacent angles alfo alfo equal alſo angle ABC angle ACB angle BAC arch bafe baſe BC is equal becauſe the angle bifected Book VII cafe centre circle ABC circumference co-fine defcribed demonftrated diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle faid fame manner fame ratio fame reaſon fecond fection fegment femicircle fhewn fimilar fince firft firſt folid fore fquare of AC ftraight line AB fuch given ſtraight line greater impoffible infcribed interfection join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepiped parallelogram perpendicular polygon prifm propofition proportionals radius rectangle contained rectilineal figure remaining angle right angles ſpace ſpherical triangle ſquare tangent thefe THEOR theſe thoſe touches the circle triangle ABC wherefore
Popular passages
Page 18 - 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 155 - 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 17 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Page 3 - 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 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 12 - ABC: and it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore the angles at the base, &c.
Page 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 156 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Page 44 - 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...