The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
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Αποτελέσματα 1 - 5 από τα 85.
Σελίδα 18
... sides equal is called equilateral . B E 45. DEF . A figure which has all its angles equal is called equiangular . F B E We shall shew that an equilateral triangle is also equiangular . A four - sided figure which is equilateral is not ...
... sides equal is called equilateral . B E 45. DEF . A figure which has all its angles equal is called equiangular . F B E We shall shew that an equilateral triangle is also equiangular . A four - sided figure which is equilateral is not ...
Σελίδα 19
... equal in all respects , it is meant that each part of one triangle is equal to the corresponding part of the other ... sides and the angle between them . [ Prop . 4 ] II . Three sides . [ Prop . 8 ] III . Two angles and one side . [ Prop ...
... equal in all respects , it is meant that each part of one triangle is equal to the corresponding part of the other ... sides and the angle between them . [ Prop . 4 ] II . Three sides . [ Prop . 8 ] III . Two angles and one side . [ Prop ...
Σελίδα 20
... sides of the one equal to two sides of the other each to each and also the angles con- tained by those sides equal , the two triangles are equal in all respects . Let ABC , DEF represent two triangles , in which AB is equal to DE , AC equal ...
... sides of the one equal to two sides of the other each to each and also the angles con- tained by those sides equal , the two triangles are equal in all respects . Let ABC , DEF represent two triangles , in which AB is equal to DE , AC equal ...
Σελίδα 21
... equal to it . 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 ...
... equal to it . 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 ...
Σελίδα 22
... sides in the triangles ABE , CBE ; therefore AE = CE . Q.E.D. EXAMPLES I. 1. In the figure of Example i on page 21 , the lines BD , CE are equal and the angles DBC , ECB are equal ; prove that the triangle DBC can coincide with the ...
... sides in the triangles ABE , CBE ; therefore AE = CE . Q.E.D. EXAMPLES I. 1. In the figure of Example i on page 21 , the lines BD , CE are equal and the angles DBC , ECB are equal ; prove that the triangle DBC can coincide with the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Σελίδα 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.
Σελίδα 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.