Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six books |
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Page 58
... multiple of a given square : or equal to the difference of two given squares . The truth of this proposition may be exhibited to the eye in some particular instances . As in the case of that right - angled triangle whose three sides are ...
... multiple of a given square : or equal to the difference of two given squares . The truth of this proposition may be exhibited to the eye in some particular instances . As in the case of that right - angled triangle whose three sides are ...
Page 100
... multiples of the same linear unit . If , however , the sides of rectangles are supposed to be divisible into an exact number of linear units , a numerical representation for the area of a rectangle may be deduced . On two lines at right ...
... multiples of the same linear unit . If , however , the sides of rectangles are supposed to be divisible into an exact number of linear units , a numerical representation for the area of a rectangle may be deduced . On two lines at right ...
Page 192
... multiple of the angles of three regular figures only , namely , the trigon , the square , and the hexagon , can fill up space round a point in a plane . It has been shewn that the interior angle of any regular polygon of n sides in ...
... multiple of the angles of three regular figures only , namely , the trigon , the square , and the hexagon , can fill up space round a point in a plane . It has been shewn that the interior angle of any regular polygon of n sides in ...
Page 193
... multiple of the interior angles of any other regular polygon , will be found to be in excess above , or in defect from four right angles . The equilateral triangle or trigon , the square or tetragon , the penta- gon , and the hexagon ...
... multiple of the interior angles of any other regular polygon , will be found to be in excess above , or in defect from four right angles . The equilateral triangle or trigon , the square or tetragon , the penta- gon , and the hexagon ...
Page 204
... multiple of a less , when the greater is measured by the less , that is , ' when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less , that is , ' when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
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Common terms and phrases
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
Popular passages
Page 54 - If two triangles have two sides of the one equal to two sides of the...
Page 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...
Page 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.
Page 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.
Page 18 - Any two angles of a triangle are together less than two right angles.
Page 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.
Page 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.
Page 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.
Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 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...