The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
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Σελίδα 38
... radius . 63. A finite straight line drawn through the centre of a circle and terminated both ways by the circle is called a diameter . 64 . B The length of a circle is called its circumference . Thus in the figure ACBD is a circle ; O ...
... radius . 63. A finite straight line drawn through the centre of a circle and terminated both ways by the circle is called a diameter . 64 . B The length of a circle is called its circumference . Thus in the figure ACBD is a circle ; O ...
Σελίδα 39
... radius . When we say that we must assume that we can draw a straight line etc. , we mean that we are about to describe a system of theoretical geometrical drawing which we could actually carry out provided we could actually draw a ...
... radius . When we say that we must assume that we can draw a straight line etc. , we mean that we are about to describe a system of theoretical geometrical drawing which we could actually carry out provided we could actually draw a ...
Σελίδα 41
... radius of the circle . EXAMPLES VII . 1. AB , AC are two given straight lines terminated at A ; AB is greater than AC ; cut off a part from AB equal to AC . 2. AB is a given straight line and C is a given point ; draw from A a straight ...
... radius of the circle . EXAMPLES VII . 1. AB , AC are two given straight lines terminated at A ; AB is greater than AC ; cut off a part from AB equal to AC . 2. AB is a given straight line and C is a given point ; draw from A a straight ...
Σελίδα 42
... radius describe the circle BCD . With B as centre and BA as a radius describe the circle ACE . Let C be a point in which the two circles intersect . Join CA , CB . Then the figure ACB is an equilateral triangle such as is required ...
... radius describe the circle BCD . With B as centre and BA as a radius describe the circle ACE . Let C be a point in which the two circles intersect . Join CA , CB . Then the figure ACB is an equilateral triangle such as is required ...
Σελίδα 43
... radius BA describe the circle ADE . With centre C and radius CA describe the circle ADF . Let D be the second point in which the circles intersect . Join BD , CD . Then BDC is a triangle such as is required . Proof . Because BA , BD are ...
... radius BA describe the circle ADE . With centre C and radius CA describe the circle ADF . Let D be the second point in which the circles intersect . Join BD , CD . Then BDC is a triangle such as is required . Proof . Because BA , BD are ...
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.