Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 Seiten |
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Seite 43
... intersection of two lines is a point , and that two lines can intersect each other in one point only . Def . IV . The straight line or right line is a term so clear and intel- ligible as to be incapable of becoming more so by formal ...
... intersection of two lines is a point , and that two lines can intersect each other in one point only . Def . IV . The straight line or right line is a term so clear and intel- ligible as to be incapable of becoming more so by formal ...
Seite 44
... intersect one another , or which when produced would intersect , are said to be inclined to one another , and the inclination of the two lines is determined by the angle which they make with one another . Def . x . It may be here ...
... intersect one another , or which when produced would intersect , are said to be inclined to one another , and the inclination of the two lines is determined by the angle which they make with one another . Def . x . It may be here ...
Seite 51
... intersect each other in two points ; and it is obvious from the two circles cutting each other , in two points , one on each side of the given line , that two equilateral triangles may be formed on the given line . Prop . II . When the ...
... intersect each other in two points ; and it is obvious from the two circles cutting each other , in two points , one on each side of the given line , that two equilateral triangles may be formed on the given line . Prop . II . When the ...
Seite 54
... intersect each other in two points . Prop . XXIII . CD might be taken equal to CE , and the construction effected by means of an isosceles triangle . It would , however , be less general than Euclid's , but is more convenient in ...
... intersect each other in two points . Prop . XXIII . CD might be taken equal to CE , and the construction effected by means of an isosceles triangle . It would , however , be less general than Euclid's , but is more convenient in ...
Seite 55
... intersections , as in the figure , BEF , EFC are alternate angles as well as the angles AEF , EFD . Prop . xxvIII ... intersect one another cannot be both parallel to the same straight line . " This apparently more simple axiom follows ...
... intersections , as in the figure , BEF , EFC are alternate angles as well as the angles AEF , EFD . Prop . xxvIII ... intersect one another cannot be both parallel to the same straight line . " This apparently more simple axiom follows ...
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Häufige Begriffe und Wortgruppen
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
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Seite 54 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 18 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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...