Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Del 11871 |
Inni boken
Resultat 1-5 av 26
Side 19
... , BAC = L BDC , Then , as in Case I. , the equality of the original triangles may be proved . Q. E. D. PROPOSITION IX . To bisect a given angle . A 2-2 BOOK I. PROP . C. 19 CASE II. When the line joining the vertices does ...
... , BAC = L BDC , Then , as in Case I. , the equality of the original triangles may be proved . Q. E. D. PROPOSITION IX . To bisect a given angle . A 2-2 BOOK I. PROP . C. 19 CASE II. When the line joining the vertices does ...
Side 20
... bisect BAC . For in As AFD , AFE , :: AD = AE , and AF is common , and FD = FE , : . LDAF LEAF , that is , BAC is bisected by AF . I. C. Q.E.F. Ex . 1. Shew that we can prove this Proposition by means of Prop . IV . and Prop . A ...
... bisect BAC . For in As AFD , AFE , :: AD = AE , and AF is common , and FD = FE , : . LDAF LEAF , that is , BAC is bisected by AF . I. C. Q.E.F. Ex . 1. Shew that we can prove this Proposition by means of Prop . IV . and Prop . A ...
Side 21
... bisect AB . On AB describe an equilat . △ ACB . Bisect ACB by the st . line CD meeting AB in D ; I. 9 . then AB shall be bisected in D. For in As ACD , BCD , * AC = BC , and CD is common , and 4 ACD = 4 BCD , .. AD = BD ; .. AB is bisected ...
... bisect AB . On AB describe an equilat . △ ACB . Bisect ACB by the st . line CD meeting AB in D ; I. 9 . then AB shall be bisected in D. For in As ACD , BCD , * AC = BC , and CD is common , and 4 ACD = 4 BCD , .. AD = BD ; .. AB is bisected ...
Side 22
... bisected by AF . Ex . 2. If O be the point in which two lines , bisecting AB and AC , two sides of an equilateral triangle , at right angles , meet ; shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular ...
... bisected by AF . Ex . 2. If O be the point in which two lines , bisecting AB and AC , two sides of an equilateral triangle , at right angles , meet ; shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular ...
Side 23
... Bisect EF in O , and join CE , CO , CF. Then CO shall be to AB . For in As COE , COF , · ::: EO = FO , and CO is common , and CE = CF , L COEL COF ; . CO is to AB . I. C. Def 9 . Q.E.F. Ex . 1. If the straight line were not of unlimited ...
... Bisect EF in O , and join CE , CO , CF. Then CO shall be to AB . For in As COE , COF , · ::: EO = FO , and CO is common , and CE = CF , L COEL COF ; . CO is to AB . I. C. Def 9 . Q.E.F. Ex . 1. If the straight line were not of unlimited ...
Andre utgaver - Vis alle
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.