Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 σελίδες |
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Σελίδα 153
... chord is the straight line joining the extremities of an arc . Every chord except a diameter divides a circle into two unequal segments , one greater than , and the other less than a semicircle . And in the same manner , two radii drawn ...
... chord is the straight line joining the extremities of an arc . Every chord except a diameter divides a circle into two unequal segments , one greater than , and the other less than a semicircle . And in the same manner , two radii drawn ...
Σελίδα 156
... chords to the given arc , bisecting them , and from the points of bisection drawing perpendiculars . The point in which they meet will be the center of the circle . This problem is equi- valent to that of finding a point equally distant ...
... chords to the given arc , bisecting them , and from the points of bisection drawing perpendiculars . The point in which they meet will be the center of the circle . This problem is equi- valent to that of finding a point equally distant ...
Σελίδα 157
... chord , secant . 2. How does a sector differ in form from a segment of a circle ? Are they in any case coincident ? 3. What is Euclid's criterion of the equality of two circles ? What is meant by a given circle ? How many points are ...
... chord , secant . 2. How does a sector differ in form from a segment of a circle ? Are they in any case coincident ? 3. What is Euclid's criterion of the equality of two circles ? What is meant by a given circle ? How many points are ...
Σελίδα 158
... chord of an arc be twelve inches long , and be divided into two segments of eight and four inches by another chord : what is the length of the latter chord , if one of its segments be two inches ? 20. What is the radius of that circle ...
... chord of an arc be twelve inches long , and be divided into two segments of eight and four inches by another chord : what is the length of the latter chord , if one of its segments be two inches ? 20. What is the radius of that circle ...
Σελίδα 160
... chords of a circle at right angles to each other , prove that ti sum of the arcs AC , BD is equal to the sum of the arcs AD , BC . Draw the diameter FGH parallel to AB , and cutting CD in H. A D B E H C Then the arcs FDG and FCG are ...
... chords of a circle at right angles to each other , prove that ti sum of the arcs AC , BD is equal to the sum of the arcs AD , BC . Draw the diameter FGH parallel to AB , and cutting CD in H. A D B E H C Then the arcs FDG and FCG are ...
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A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Σελίδα 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 18 - Any two angles of a triangle are together less than two right angles.
Σελίδα 266 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...