The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 páginas |
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Página 7
... double point ; or , a larger point ; for a point has no magnitude . They simply ' coincide ' or become one point . If a line is applied to another line so as to ' coincide ' they do not make a thicker line ; for a line has no thickness ...
... double point ; or , a larger point ; for a point has no magnitude . They simply ' coincide ' or become one point . If a line is applied to another line so as to ' coincide ' they do not make a thicker line ; for a line has no thickness ...
Página 11
... double that of another when the second , if applied twice to the first , then has completely covered the whole of its surface and has not been applied to any part of the first more than once . 28. A figure consisting only of finite ...
... double that of another when the second , if applied twice to the first , then has completely covered the whole of its surface and has not been applied to any part of the first more than once . 28. A figure consisting only of finite ...
Página 33
... double of ACB ; prove that the line which bisects the angle ABC cuts AC in D so that BD = CD . 4. In the figure on page 21 , if BE , CD intersect in F , prove that BF = CF . 5. The angles at B , C of an isosceles triangle ABC are ...
... double of ACB ; prove that the line which bisects the angle ABC cuts AC in D so that BD = CD . 4. In the figure on page 21 , if BE , CD intersect in F , prove that BF = CF . 5. The angles at B , C of an isosceles triangle ABC are ...
Página 44
... double of the given straight line . 8. Upon a given straight line describe a triangle such that one of its sides is double a given straight line and the third side is three times the same straight line . 9. Shew that in Question 8 the ...
... double of the given straight line . 8. Upon a given straight line describe a triangle such that one of its sides is double a given straight line and the third side is three times the same straight line . 9. Shew that in Question 8 the ...
Página 47
... double of the given line , shew that then the figure may be drawn in such a way that the two circles are equal . 9. Prove that in the figure of Proposition 2 when AB is greater than twice BC the circle last described is always greater ...
... double of the given line , shew that then the figure may be drawn in such a way that the two circles are equal . 9. Prove that in the figure of Proposition 2 when AB is greater than twice BC the circle last described is always greater ...
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.