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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Results 1-5 of 32
Page 10
... triangle on a given straight B E Let AB be the given st . line . It is required to describe an equilat . △ on AB ... ABC be an equilat . A. For A is the centre of BCD , .. AC = AB . Def . 13 . And B is the centre of OACE , .. BC = AB . Def .
... triangle on a given straight B E Let AB be the given st . line . It is required to describe an equilat . △ on AB ... ABC be an equilat . A. For A is the centre of BCD , .. AC = AB . Def . 13 . And B is the centre of OACE , .. BC = AB . Def .
Page 14
... triangle may be moved from one place , turned over , and put down in another place , without altering the relative ... ABC and DEF to be two given angles . A LV B F Suppose the arm BC to be placed on the arm EF , and the vertex B on the ...
... triangle may be moved from one place , turned over , and put down in another place , without altering the relative ... ABC and DEF to be two given angles . A LV B F Suppose the arm BC to be placed on the arm EF , and the vertex B on the ...
Page 16
... triangle ABC , let AC = AB . ( fig . 1. ) Then must L ABC = LACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in fig . 2 , and designate the angular points A ' , B ' , C ' . Then in ...
... triangle ABC , let AC = AB . ( fig . 1. ) Then must L ABC = LACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in fig . 2 , and designate the angular points A ' , B ' , C ' . Then in ...
Page 17
... triangles be equal in all respects . B E In As ABC , DEF , let ABC DEF , and L ACB = LDFE , and BC = EF . Then must AB = DE , and AC ÷ DF , and ↳ BAČ = 4 EDF . L For if △ DEF be applied to △ ABC , so that E coincides with B , and EF ...
... triangles be equal in all respects . B E In As ABC , DEF , let ABC DEF , and L ACB = LDFE , and BC = EF . Then must AB = DE , and AC ÷ DF , and ↳ BAČ = 4 EDF . L For if △ DEF be applied to △ ABC , so that E coincides with B , and EF ...
Page 24
... ABC is any triangle . In BA , or BA produced , find a point D such that BD = CD . 7. The equal sides AB , AC , of an isosceles triangle ABC , are produced to points F and G , so that AF - AG . BG and CF are joined , and H is the point ...
... ABC is any triangle . In BA , or BA produced , find a point D such that BD = CD . 7. The equal sides AB , AC , of an isosceles triangle ABC , are produced to points F and G , so that AF - AG . BG and CF are joined , and H is the point ...
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 acute adjacent alternate angles equal angular points applied base bisected Book called centre circle coincide common construction describe diagonal difference distance divided double draw equal equidistant Euclid Exercises extremities fall figure four Geometry given point given straight line greater half Hence interior angles intersect isosceles triangle join length less Let ABC line joining magnitude measure meet method NOTE obtuse opposite sides parallel parallelogram perpendicular placed polygon position Post Postulate PROBLEM produced proof Prop PROPOSITION proved Q. E. D. Ex quadrilateral rectangle contained respects right angles Shew shewn sides square sum of sqq suppose Surface Take taken THEOREM triangle ABC triangles are equal unequal vertex vertical whole
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.