Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Μέρος 11871 |
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Σελίδα 10
Euclides James Hamblin Smith. line . SECTION I. On the Properties of Triangles . PROPOSITION I. PROBLEM . To describe an equilateral triangle ... ABC be an equilat . A. For A is the centre of BCD , .. AC = AB . Def . 13 . And B is the centre ...
Euclides James Hamblin Smith. line . SECTION I. On the Properties of Triangles . PROPOSITION I. PROBLEM . To describe an equilateral triangle ... ABC be an equilat . A. For A is the centre of BCD , .. AC = AB . Def . 13 . And B is the centre ...
Σελίδα 14
... triangles are equal , if they can be so placed that their sides coincide in di- rection and magnitude . In the application of the test of equality by this Method of Superposition , we assume that an angle or a triangle ... ABC and DEF to be ...
... triangles are equal , if they can be so placed that their sides coincide in di- rection and magnitude . In the application of the test of equality by this Method of Superposition , we assume that an angle or a triangle ... ABC and DEF to be ...
Σελίδα 16
... triangle ABC , let AC = AB . ( fig . 1. ) Then must LABC = 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 As ABC ...
... triangle ABC , let AC = AB . ( fig . 1. ) Then must LABC = 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 As ABC ...
Σελίδα 17
... triangles be equal in all respects . B E In as ABC , DEF , let ABC = L DEF , and △ ACB = △ DFE , and BC = EF . Then must AB = DE , and AC ÷ DF , and △ BAC = △ EDF . 4 For if a DEF be applied to △ ABC , so that E coincides with B ...
... triangles be equal in all respects . B E In as ABC , DEF , let ABC = L DEF , and △ ACB = △ DFE , and BC = EF . Then must AB = DE , and AC ÷ DF , and △ BAC = △ EDF . 4 For if a DEF be applied to △ ABC , so that E coincides with B ...
Σελίδα 24
... triangle ABC , are produced to points F and G , so that AF - AG . BG and CF are joined , and H is the point of their intersection . Prove that BH = CH , and also that the angle at A is bisected by AH . 8. BAC , BDC are isosceles triangles ...
... triangle ABC , are produced to points F and G , so that AF - AG . BG and CF are joined , and H is the point of their intersection . Prove that BH = CH , and also that the angle at A is bisected by AH . 8. BAC , BDC are isosceles triangles ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.