Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
Results 1-5 of 87
Page 5
... base . The angular point opposite to the base of a triangle is called the vertex ; and the angle at the vertex , the vertical angle . 48. The altitude of a triangle , or a parallelogram , is the length of a perpendicular drawn from the ...
... base . The angular point opposite to the base of a triangle is called the vertex ; and the angle at the vertex , the vertical angle . 48. The altitude of a triangle , or a parallelogram , is the length of a perpendicular drawn from the ...
Page 9
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF ( Def . 3 ) , and shall be equal to it . Therefore , also , the whole FIRST ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF ( Def . 3 ) , and shall be equal to it . Therefore , also , the whole FIRST ...
Page 10
... base will also be equal . For BG and EH will coincide , and therefore the angle GBC is equal to the angle HEF . PROPOSITION V. THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides ...
... base will also be equal . For BG and EH will coincide , and therefore the angle GBC is equal to the angle HEF . PROPOSITION V. THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides ...
Page 11
... base are equal . It is evident that some line will bisect the vertical angle ; and although the method of doing it ... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ( I. 4 ) , the less equal to the ...
... base are equal . It is evident that some line will bisect the vertical angle ; and although the method of doing it ... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ( I. 4 ) , the less equal to the ...
Page 12
... base CD , are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , if CB were equal to DB ...
... base CD , are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , if CB were equal to DB ...
Other editions - View all
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde No preview available - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde No preview available - 2018 |
Common terms and phrases
ABCD adjacent angles angle ABC angle ACB angle BAC apothem base BC BC is equal bisected centre Chambers's chord circle ABC circumference Const cosec cosine described diameter divided double draw equal angles equal to twice equiangular equilateral equilateral polygon equimultiples exterior angle fore given line given point given straight line gnomon greater hence hypotenuse inscribed isosceles triangle less line drawn multiple number of sides opposite angle parallel parallelogram perimeter perpendicular polygon produced proportional PROPOSITION prove radius ratio rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle segment semiperimeter shewn similar sine square on AC straight line AC tangent THEOREM third touches the circle triangle ABC triangle DEF twice the rectangle vertical angle wherefore
Popular passages
Page 23 - 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. either the sides adjacent to the equal...
Page 52 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Page 51 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 53 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...
Page 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 29 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 117 - And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to d ', then, for shortness...
Page 13 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Page 159 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Page 60 - CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.