Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Σελίδα 30
... ABCD and EBCF ( see the 2d and 3d figures ) upon the same base BC , and between the same parallels AF , BC ; to prove that the parallelogram ABCD is equal to the parallelogram EBCF . ( Dem . ) If the sides AD and DF , of the parallelograms ...
... ABCD and EBCF ( see the 2d and 3d figures ) upon the same base BC , and between the same parallels AF , BC ; to prove that the parallelogram ABCD is equal to the parallelogram EBCF . ( Dem . ) If the sides AD and DF , of the parallelograms ...
Σελίδα 31
... ABCD ( I. 35 ) , because it is upon the same base BC , and between the same parallels BC and AH . For a like reason , the paral- lelogram EFGH is equal to the same parallelogram EBCH ; therefore ( Ax . 1 ) the parallelogram ABCD is ...
... ABCD ( I. 35 ) , because it is upon the same base BC , and between the same parallels BC and AH . For a like reason , the paral- lelogram EFGH is equal to the same parallelogram EBCH ; therefore ( Ax . 1 ) the parallelogram ABCD is ...
Σελίδα 34
... ABCD and the triangle EBC upon the same base BC , and between the same parallels BC , AE ; to prove that the parallelogram ABCD is double of the triangle EBC . ( Const . ) Join AC . ( Dem . ) Then the tri- angle ABC is equal to the ...
... ABCD and the triangle EBC upon the same base BC , and between the same parallels BC , AE ; to prove that the parallelogram ABCD is double of the triangle EBC . ( Const . ) Join AC . ( Dem . ) Then the tri- angle ABC is equal to the ...
Σελίδα 35
... ABCD , of which the diagonal is AC ; and let EH and FG be the parallelograms about AC , that is , through which AC passes ; and BK and KD the other paral- lelograms which make up the whole figure ABCD , which are therefore called the ...
... ABCD , of which the diagonal is AC ; and let EH and FG be the parallelograms about AC , that is , through which AC passes ; and BK and KD the other paral- lelograms which make up the whole figure ABCD , which are therefore called the ...
Σελίδα 36
... ABCD , and the rectilineal angle E. It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. ( Const . ) Join DB , and describe ( I. 42 ) the parallelogram FH equal to the triangle ABD , and having the ...
... ABCD , and the rectilineal angle E. It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. ( Const . ) Join DB , and describe ( I. 42 ) the parallelogram FH equal to the triangle ABD , and having the ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.