The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 19
... BC = EF ; the angle BAC EDF , the angle ABCDEF , the angle BCA = EFD ; and the area enclosed by ABC - area enclosed ... side . [ Prop . 26 ] At the conclusion of the proof of a Geometrical State- ment , or Theorem , it is usual to put ...
... BC = EF ; the angle BAC EDF , the angle ABCDEF , the angle BCA = EFD ; and the area enclosed by ABC - area enclosed ... side . [ Prop . 26 ] At the conclusion of the proof of a Geometrical State- ment , or Theorem , it is usual to put ...
Σελίδα 23
... BC , CD are three straight lines such that AB = CD and the angle ABC = the angle BCD ; prove that AC = BD . 7. ABC ... side makes equal angles with that side , the two other sides of the triangle are equal . 13. Prove by the method of ...
... BC , CD are three straight lines such that AB = CD and the angle ABC = the angle BCD ; prove that AC = BD . 7. ABC ... side makes equal angles with that side , the two other sides of the triangle are equal . 13. Prove by the method of ...
Σελίδα 24
... side AC ; it is required to prove that the angle ACB , opposite to AB , is equal to the angle ABC , opposite to AC . B E F Let DEF be a triangle equal to ABC in all respects ; so that the sides BC ... angle DEF coincides with the angle ACB ...
... side AC ; it is required to prove that the angle ACB , opposite to AB , is equal to the angle ABC , opposite to AC . B E F Let DEF be a triangle equal to ABC in all respects ; so that the sides BC ... angle DEF coincides with the angle ACB ...
Σελίδα 27
... B , A , C to F , D , E respectively ; so that the angle ABC , or the angle ACB can be made to coincide with the same angle DEF . EXAMPLES II . 1. ABC is a triangle in which AB = AC and in the side BC two points D , E are taken such that ...
... B , A , C to F , D , E respectively ; so that the angle ABC , or the angle ACB can be made to coincide with the same angle DEF . EXAMPLES II . 1. ABC is a triangle in which AB = AC and in the side BC two points D , E are taken such that ...
Σελίδα 28
... angle ABC is equal to the angle DEF , the angle ACB is equal to the angle DFE and the side BC is equal to the side EF ; it is required to prove that the triangles ABC , DEF are equal in all respects . B F Let the triangle ABC be applied ...
... angle ABC is equal to the angle DEF , the angle ACB is equal to the angle DFE and the side BC is equal to the side EF ; it is required to prove that the triangles ABC , DEF are equal in all respects . B F Let the triangle ABC be applied ...
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.