The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 páginas |
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Página 21
... Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively , then the angle HBC is equal to the angle LEF ...
... Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively , then the angle HBC is equal to the angle LEF ...
Página 25
... Wherefore , if two sides of a triangle , etc. Q.E.D. 52. Corollary . If the two equal sides of an isosceles triangle be produced then the angles on the other side of the base are equal to each other . In the figure of Proposition 5 ...
... Wherefore , if two sides of a triangle , etc. Q.E.D. 52. Corollary . If the two equal sides of an isosceles triangle be produced then the angles on the other side of the base are equal to each other . In the figure of Proposition 5 ...
Página 26
... equal . But the angles ACD , ABE have been proved to be equal ; therefore the remainders ACB , ABC are also equal . Wherefore , the angles at the base of an isosceles triangle , etc. Q.E.D. NOTE . The proof of Prop . 5 , on 26 EUCLID .
... equal . But the angles ACD , ABE have been proved to be equal ; therefore the remainders ACB , ABC are also equal . Wherefore , the angles at the base of an isosceles triangle , etc. Q.E.D. NOTE . The proof of Prop . 5 , on 26 EUCLID .
Página 29
... Wherefore , if two triangles have two angles , etc. Q.E.D. EXAMPLES III . 1. The angle ABC is bisected by the line BD . From D the lines DA , DC are drawn making the angles BDA , BDC equal ; prove that DA , DC are equal . 2. Two angles ...
... Wherefore , if two triangles have two angles , etc. Q.E.D. EXAMPLES III . 1. The angle ABC is bisected by the line BD . From D the lines DA , DC are drawn making the angles BDA , BDC equal ; prove that DA , DC are equal . 2. Two angles ...
Página 31
... Wherefore , if two sides of a triangle , etc. Q.E.D. 56. Corollary . If two sides of a triangle are produced and the angles thus made with the base of the triangle are equal , then the two first sides of the triangle are equal to each ...
... Wherefore , if two sides of a triangle , etc. Q.E.D. 56. Corollary . If two sides of a triangle are produced and the angles thus made with the base of the triangle are equal , then the two first sides of the triangle are equal to each ...
Términos y frases comunes
ABC is equal adjacent angles alternate angles angle ABC angle ACB angle BAC angle equal angles FAB angular point area of ABC base BC bisectors bisects the angle centre coincide Consider the triangles Construction corresponding angle DEF are equal describe a triangle diagonal equal angles equal area equal in area equal respectively equal to BC equidistant equilateral triangle exterior angle finite straight line given angle given finite straight given parallelogram given point given straight line given triangle greater included angle interior opposite angle intersect isosceles triangle line BC middle point opposite sides perpendicular plane produced Prop Proposition Q.E.D. EXAMPLES quadrilateral radius rectilineal figure required to prove rhombus right angles right-angled triangle Shew side BC sides equal square straight angle surface third side triangle ABC triangle DEF triangles are equal Wherefore
Pasajes populares
Página 28 - 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.
Página 72 - 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.
Página 48 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Página 151 - 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.
Página 118 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Página 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Página 114 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 125 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Página 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.