The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
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Αποτελέσματα 1 - 5 από τα 50.
Σελίδα
... angle . If there is a line which divides the angle ABC into two equal parts , it must cut the line AC in some point E ; and then by Prop . 4 the triangles ABE , CBE are equal in all respects . Similarly we may assume that a triangle DEF ...
... angle . If there is a line which divides the angle ABC into two equal parts , it must cut the line AC in some point E ; and then by Prop . 4 the triangles ABE , CBE are equal in all respects . Similarly we may assume that a triangle DEF ...
Σελίδα 17
... triangle has three angles . Hence its name . The angles of the triangle ABC are CAB , BCA , ABC . The points A , B , C are called the angular points of the triangle ABC . A triangle encloses a certain amount of surface called its area .
... triangle has three angles . Hence its name . The angles of the triangle ABC are CAB , BCA , ABC . The points A , B , C are called the angular points of the triangle ABC . A triangle encloses a certain amount of surface called its area .
Σελίδα 19
... triangle . B A Thus when the triangles ABC , DEF are equal in all respects then AB = DE , AC = DF , BC = EF ; the angle BAC EDF , the angle ABCDEF , the angle BCA = EFD ; and the area enclosed by ABC - area enclosed by DEF . This would ...
... triangle . B A Thus when the triangles ABC , DEF are equal in all respects then AB = DE , AC = DF , BC = EF ; the angle BAC EDF , the angle ABCDEF , the angle BCA = EFD ; and the area enclosed by ABC - area enclosed by DEF . This would ...
Σελίδα 20
... triangles have two 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 ...
... triangles have two 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 ...
Σελίδα 21
... ABC coincides with the corresponding part of the triangle DEF and is therefore equal to it . Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ... angle ABC is bisected by the PROPOSITION 4 . 21.
... ABC coincides with the corresponding part of the triangle DEF and is therefore equal to it . Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ... angle ABC is bisected by the PROPOSITION 4 . 21.
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.