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 |
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Page 7
... shew hereafter , be deduced from a more simple Postulate . The student must defer the consideration of this Postulate , till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axioms or ...
... shew hereafter , be deduced from a more simple Postulate . The student must defer the consideration of this Postulate , till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axioms or ...
Page 12
... Shew that if straight lines be drawn from A and B in the diagram of Prop . I. to the other point in which the circles intersect , another equilateral triangle will be described on АВ . 2. By a similar construction to that in Prop . 1 ...
... Shew that if straight lines be drawn from A and B in the diagram of Prop . I. to the other point in which the circles intersect , another equilateral triangle will be described on АВ . 2. By a similar construction to that in Prop . 1 ...
Page 20
... Shew that we can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
... Shew that we can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
Page 22
... Shew that in the diagram of Prop . ix . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
... Shew that in the diagram of Prop . ix . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
Page 24
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that _BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a - given straight line find a ...
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that _BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a - given straight line find a ...
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...