Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Part 11871 |
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Page 8
... double of the same thing are equal to one another . VII . Things which are halves of the same thing are equal to one another . VIII . Magnitudes which coincide with one another are equal to one another . IX . The whole is greater than ...
... double of the same thing are equal to one another . VII . Things which are halves of the same thing are equal to one another . VIII . Magnitudes which coincide with one another are equal to one another . IX . The whole is greater than ...
Page 33
... If one side of a triangle be bisected , the sum of the two other sides shall be more than double of the line joining the vertex and the point of bisection . S. E. 3 PROPOSITION XXI . THEOREM . If , from the ends BOOK I. PROP . XX . 33.
... If one side of a triangle be bisected , the sum of the two other sides shall be more than double of the line joining the vertex and the point of bisection . S. E. 3 PROPOSITION XXI . THEOREM . If , from the ends BOOK I. PROP . XX . 33.
Page 35
... . 13 . Def . 13 . Q. E. F. Ex . Draw an isosceles triangle having each of the equal sides double of the base . PROPOSITION XXIII . PROBLEM . At a given point in 3-2 BOOK I. PROP . XXII . 35 Ex. 2. Shew that the sum of the straight ...
... . 13 . Def . 13 . Q. E. F. Ex . Draw an isosceles triangle having each of the equal sides double of the base . PROPOSITION XXIII . PROBLEM . At a given point in 3-2 BOOK I. PROP . XXII . 35 Ex. 2. Shew that the sum of the straight ...
Page 53
... double of the angle AED . Ex . 4. If the straight lines bisecting the angles at the base of an isosceles triangle be produced to meet ; shew that they will contain an angle equal to an exterior angle at the base of the triangle . Ex . 5 ...
... double of the angle AED . Ex . 4. If the straight lines bisecting the angles at the base of an isosceles triangle be produced to meet ; shew that they will contain an angle equal to an exterior angle at the base of the triangle . Ex . 5 ...
Page 55
... double that of its exterior angles ? Ex . 5. How many sides has an equiangular polygon , four of whose angles are together equal to seven right angles ? PROPOSITION XXXIII . THEOREM . The straight lines which join the extremities of two ...
... double that of its exterior angles ? Ex . 5. How many sides has an equiangular polygon , four of whose angles are together equal to seven right angles ? PROPOSITION XXXIII . THEOREM . The straight lines which join the extremities of two ...
Other editions - View all
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2016 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2018 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2015 |
Common terms and phrases
AB=DE ABCD AC=DF adjacent angles angle contained angles equal angular points base BC centre coincide describe the sq diagonal draw a straight equal angles equal bases equilat equilateral triangle Euclid Geometry given angle given point given st given straight line half a rt hypotenuse interior angles intersect isosceles triangle LABC LADC LAGH Let ABC Let the st lines be drawn magnitude measure meet middle points opposite angles opposite sides parallel straight lines parallelogram perpendicular polygon Postulate PROBLEM produced proved Q. E. D. Ex quadrilateral rectangle contained reqd rhombus right angles Shew shewn sides equal straight line joining straight lines drawn sum of sqq Take any pt THEOREM together=two rt trapezium triangle ABC triangles are equal twice rect twice sq vertex vertical angle
Popular passages
Page 52 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 83 - 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, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Page 17 - 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 48 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Page 26 - 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 86 - 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 90 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page 106 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
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 of the line between the points of section, is equal to the square of half the line.