The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 Seiten |
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Seite 18
... shew that an equilateral triangle is also equiangular . A four - sided figure which is equilateral is not necessarily also equiangular . 46. DEF . A triangle which has two sides equal is called isosceles . A NOTE . The word base is ...
... shew that an equilateral triangle is also equiangular . A four - sided figure which is equilateral is not necessarily also equiangular . 46. DEF . A triangle which has two sides equal is called isosceles . A NOTE . The word base is ...
Seite 22
... shew that AC is bisected at the point in which it meets BD . B A Let BD meet AC in E. Consider the triangles ABE , CBE . We have BA = BC , and the angle ABE = the angle CBE ; so that the two sides AB , BE and their included angle ABE of ...
... shew that AC is bisected at the point in which it meets BD . B A Let BD meet AC in E. Consider the triangles ABE , CBE . We have BA = BC , and the angle ABE = the angle CBE ; so that the two sides AB , BE and their included angle ABE of ...
Seite 23
... shew that when two sides of a triangle are equal , the angles opposite those sides are also equal . 6. AB , BC , CD are three straight lines such that AB = CD and the angle ABC = the angle BCD ; prove that AC = BD . 7. ABC is a triangle ...
... shew that when two sides of a triangle are equal , the angles opposite those sides are also equal . 6. AB , BC , CD are three straight lines such that AB = CD and the angle ABC = the angle BCD ; prove that AC = BD . 7. ABC is a triangle ...
Seite 29
... shew that the quadrilaterals are equal in all respects . 6. Two sides of each of two triangles are produced , prove that if the bases are equal and the angles on the other side of the bases equal each to each the triangles are equal in ...
... shew that the quadrilaterals are equal in all respects . 6. Two sides of each of two triangles are produced , prove that if the bases are equal and the angles on the other side of the bases equal each to each the triangles are equal in ...
Seite 33
... shew that there is a point D in AC which is equidistant from A , B , C. 9. Prove the following construction for bisecting an angle BAC ; in AB take two points D , B , and let AC = AB and in AC take E so that AE = AD ; let BE , CD ...
... shew that there is a point D in AC which is equidistant from A , B , C. 9. Prove the following construction for bisecting an angle BAC ; in AB take two points D , B , and let AC = AB and in AC take E so that AE = AD ; let BE , CD ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Seite 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.
Seite 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 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.
Seite 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.