Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
From inside the book
Results 1-5 of 35
Page 6
... shewn hereafter that a triangle can have only one of its angles either equal to , or greater than , a right angle . XXV . An ACUTE - ANGLED Triangle is one in which ALL the angles are acute . XXVI . PARALLEL STRAIGHT LINES are such as ...
... shewn hereafter that a triangle can have only one of its angles either equal to , or greater than , a right angle . XXV . An ACUTE - ANGLED Triangle is one in which ALL the angles are acute . XXVI . PARALLEL STRAIGHT LINES are such as ...
Page 26
... shewn that no other line but BD is in the same st . line with BC . .. BD is in the same st . line with BC . Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight ...
... shewn that no other line but BD is in the same st . line with BC . .. BD is in the same st . line with BC . Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight ...
Page 27
... shewn that △ AED = △ BEC . L Ax . 3 . Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines ... Shew that the bisectors of AED and BEC are in the same straight line . Ex . 2. Prove that △ AED is equal to the ...
... shewn that △ AED = △ BEC . L Ax . 3 . Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines ... Shew that the bisectors of AED and BEC are in the same straight line . Ex . 2. Prove that △ AED is equal to the ...
Page 29
... shewn that 4 BCG is greater than △ ABC . and LBCGL ACD ; .. ACD is greater than △ ABC . I. 15 . Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight lines to meet a given straight line . Ex . 2. If ...
... shewn that 4 BCG is greater than △ ABC . and LBCGL ACD ; .. ACD is greater than △ ABC . I. 15 . Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight lines to meet a given straight line . Ex . 2. If ...
Page 30
... shewn that s ABC , BAC and also that 48 BAC , ACB are together less than two rt . 4 s . NOTE 4. On the Sixth Postulate . Q. E. D. We learn from Prop . xvII . that if two straight lines BM and CN , which meet in A , are met by another ...
... shewn that s ABC , BAC and also that 48 BAC , ACB are together less than two rt . 4 s . NOTE 4. On the Sixth Postulate . Q. E. D. We learn from Prop . xvII . that if two straight lines BM and CN , which meet in A , are met by another ...
Common terms and phrases
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given point given st given straight line greater than nD hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallelogram pentagon perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rect rectangle contained reflex angle rhombus right angles segment shew shewn straight line joining subtended sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Popular passages
Page 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. Let AB be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to AB from the point c. Take any point D upon the other side of AB, and from the centre c, at the distance CD, describe (Post.
Page 82 - 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 on the line between the points of section, is equal to the square on half the line.
Page 40 - 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 161 - 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 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 5 - 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 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 35 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Page 90 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Page 265 - EQUAL parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...