The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 páginas |
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Página 22
... Question 2 E is any point in AD , prove that EB = EC . 4. Three lines AB , AC , AD are equal , and the angle BAC = CAD ; prove that BC = CD . To bisect is to divide into two equal parts . 5. Use the construction of Question 2 to shew ...
... Question 2 E is any point in AD , prove that EB = EC . 4. Three lines AB , AC , AD are equal , and the angle BAC = CAD ; prove that BC = CD . To bisect is to divide into two equal parts . 5. Use the construction of Question 2 to shew ...
Página 23
... Question 9 prove that any point in CD is equidistant from A and B. 11. A triangle ABC is turned over the line AC so as to have the new position AB'C ; prove that BB ' cuts AC in E so that the angles AEB , AEB ' are equal . 12. If the ...
... Question 9 prove that any point in CD is equidistant from A and B. 11. A triangle ABC is turned over the line AC so as to have the new position AB'C ; prove that BB ' cuts AC in E so that the angles AEB , AEB ' are equal . 12. If the ...
Página 27
... Question 6 prove that AD = BE = CF . 8. ABC is an equilateral triangle ; on the sides BC , CA , AB , are triangles DBC , ECA , FAB equal to each other in all respects and with their vertices D , E , F , on the sides of BC , CA , AB ...
... Question 6 prove that AD = BE = CF . 8. ABC is an equilateral triangle ; on the sides BC , CA , AB , are triangles DBC , ECA , FAB equal to each other in all respects and with their vertices D , E , F , on the sides of BC , CA , AB ...
Página 33
... Question 5 the triangle ABC is equi- lateral , prove that DA , DB , DC are all equal . 7. ABCD is quadrilateral such that AB = AD and the angle ABC = ADC ; prove that CB - CD . 8. The angle ABC is equal to the sum of the other two ...
... Question 5 the triangle ABC is equi- lateral , prove that DA , DB , DC are all equal . 7. ABCD is quadrilateral such that AB = AD and the angle ABC = ADC ; prove that CB - CD . 8. The angle ABC is equal to the sum of the other two ...
Página 44
... Question 4 three times as long as AC . 6. ABC is an unlimited straight line ; shew how to divide the line into any given number of equal parts each equal to a given part AB . 7. Upon a given straight line describe a triangle such that ...
... Question 4 three times as long as AC . 6. ABC is an unlimited straight line ; shew how to divide the line into any given number of equal parts each equal to a given part AB . 7. Upon a given straight line describe a triangle such that ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Página 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.
Página 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 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.
Página 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.