The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 Seiten |
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Seite
... triangles ABE , CBE are equal in all respects . Similarly we may assume that ... considered only as pictures , while the figures of the Problems should be ... believe that one of the great difficulties of Euclid as usually taught is that ...
... triangles ABE , CBE are equal in all respects . Similarly we may assume that ... considered only as pictures , while the figures of the Problems should be ... believe that one of the great difficulties of Euclid as usually taught is that ...
Seite 21
... angle HBC coincides with the angle LEF and is equal to it . Example i . ABC is a triangle such that AB = AC ; in AB , AC points D and E are taken such that AD = AE ; prove that DC = BE . Consider the triangles ABE , ACD ; we have AB AC ...
... angle HBC coincides with the angle LEF and is equal to it . Example i . ABC is a triangle such that AB = AC ; in AB , AC points D and E are taken such that AD = AE ; prove that DC = BE . Consider the triangles ABE , ACD ; we have AB AC ...
Seite 22
... 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 the triangle ABE are equal respectively to the two sides CB , BE and their included angle ...
... 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 the triangle ABE are equal respectively to the two sides CB , BE and their included angle ...
Seite 24
... Consider the triangles FDE , BAC ; because DF , DE , and their included angle FDE in the triangle FDE , are equal ... angle DEF coincides with the angle ACB and 24 EUCLID .
... Consider the triangles FDE , BAC ; because DF , DE , and their included angle FDE in the triangle FDE , are equal ... angle DEF coincides with the angle ACB and 24 EUCLID .
Seite 26
... consider the triangles ADC , AEB ; because the two sides DA , AC and their in- cluded angle DAC in the triangle ADC ... triangles ADC , AEB are equal in all respects ; so that the corresponding sides DC , EB are equal ; the corresponding ...
... consider the triangles ADC , AEB ; because the two sides DA , AC and their in- cluded angle DAC in the triangle ADC ... triangles ADC , AEB are equal in all respects ; so that the corresponding sides DC , EB are equal ; the corresponding ...
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.