The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 41
... similar theorem as regards a quadri- lateral . Can it be extended to other polygons ( figures with more sides than three ) ? The four sides of a quadrilateral are together greater than the diagonals . Are the five sides of a pentagon ...
... similar theorem as regards a quadri- lateral . Can it be extended to other polygons ( figures with more sides than three ) ? The four sides of a quadrilateral are together greater than the diagonals . Are the five sides of a pentagon ...
Page 62
... similar to Ex . 58 , 59 , with respect to a regular octagon ( eight - sided figure ) . magnitude of an exterior angle of such a figure ? angles of regular figures use Cor . II . ) ( For finding exterior PROPOSITION 33. THEOREM . The ...
... similar to Ex . 58 , 59 , with respect to a regular octagon ( eight - sided figure ) . magnitude of an exterior angle of such a figure ? angles of regular figures use Cor . II . ) ( For finding exterior PROPOSITION 33. THEOREM . The ...
Page 73
... similar to that given for the preceding Exercise . Ex . 80. - To construct a rectilineal figure equivalent to a given rectilineal figure , and having the number of its sides one less than that of the given figure , and thence to ...
... similar to that given for the preceding Exercise . Ex . 80. - To construct a rectilineal figure equivalent to a given rectilineal figure , and having the number of its sides one less than that of the given figure , and thence to ...
Page 91
... similar sets of numbers . The following tables supply two different methods of calculating an unlimited number of such : - TABLE I. Write down the natural numbers , Multiply each by 4 , • Add one to the product of each of these and the ...
... similar sets of numbers . The following tables supply two different methods of calculating an unlimited number of such : - TABLE I. Write down the natural numbers , Multiply each by 4 , • Add one to the product of each of these and the ...
Page 106
... similar one in giving names to our own . The properties of the particular trapezium discussed on p . 102 are those which belong to it solely in virtue of its being symmetrical about a diagonal . These it shares with equilateral ...
... similar one in giving names to our own . The properties of the particular trapezium discussed on p . 102 are those which belong to it solely in virtue of its being symmetrical about a diagonal . These it shares with equilateral ...
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Common terms and phrases
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Popular passages
Page 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 369 - 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 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Page 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 40 - Any two sides of a triangle are together greater than the third side.
Page 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Page 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 156 - 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...