Euclid, Βιβλίο 1W.B. Clive, 1903 - 164 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 85.
Σελίδα 9
... prove some geometrical truth . It would be impossible to prove every proposition . So after the Definitions in Book I. we get some easy propositions which are taken for granted . These are called either Postulates or Axioms . A ...
... prove some geometrical truth . It would be impossible to prove every proposition . So after the Definitions in Book I. we get some easy propositions which are taken for granted . These are called either Postulates or Axioms . A ...
Σελίδα 11
... proved equal to BF , therefore BC and AH are each equal to BF . Def . 15 Def . 15 Ax . 3 But things which are equal to the same thing are equal to one another , therefore by Axiom 1 AH is equal to BC , and it has been drawn from the ...
... proved equal to BF , therefore BC and AH are each equal to BF . Def . 15 Def . 15 Ax . 3 But things which are equal to the same thing are equal to one another , therefore by Axiom 1 AH is equal to BC , and it has been drawn from the ...
Σελίδα 13
... proved equal , because they are each equal to BF ; and in Proposition 3 AE and Care proved equal , because they are each equal to AD . This method of proof we constantly use in daily life . prove that two panes in a window are equal in ...
... proved equal , because they are each equal to BF ; and in Proposition 3 AE and Care proved equal , because they are each equal to AD . This method of proof we constantly use in daily life . prove that two panes in a window are equal in ...
Σελίδα 17
... prove that BF is equal to CG by Axiom 3 . ( 3 ) In the third part we prove the equality of the two triangles BFC and CGB by Proposition 4 . ( 4 ) In the fourth part we prove that the angle ABC is equal to the angle ACB by Axiom 3 . The ...
... prove that BF is equal to CG by Axiom 3 . ( 3 ) In the third part we prove the equality of the two triangles BFC and CGB by Proposition 4 . ( 4 ) In the fourth part we prove that the angle ABC is equal to the angle ACB by Axiom 3 . The ...
Σελίδα 19
... proved directly . The so - called proof starts by assuming the opposite to what it is required to prove . For example , in Prop . 6 we have to prove that AB is equal to AC . Euclid starts therefore by assuming that AB is not equal to AC ...
... proved directly . The so - called proof starts by assuming the opposite to what it is required to prove . For example , in Prop . 6 we have to prove that AB is equal to AC . Euclid starts therefore by assuming that AB is not equal to AC ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AC is equal adjacent angles Algebra angle ABC angle ACB angle AGH angle BAC angle EDF angle equal angle GHD Axiom base BC bisect centre circle Constr Construct a triangle contained angle depends on Prop diagonals Divide a given draw a line equal in area equal to AC equal to twice equilateral triangle Euclid exterior angle figure of Prop geometrical given angle given line given point given straight line given triangle gnomon greater hypotenuse interior opposite angle isosceles triangle join length Let the straight M.A. Lond measure middle point opposite sides parallel to BC parallelogram produced quadrilateral quadrilateral figure rectangle AB rectangle AQ rectangle contained rhombus right angles right-angled triangle side AC sides equal square on AC theorem triangle ABC triangle DEF twice the rectangle UNIVERSITY TUTORIAL SERIES vertex
Δημοφιλή αποσπάσματα
Σελίδα 45 - 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.
Σελίδα 126 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 31 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 138 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 66 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 130 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 99 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 26 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 63 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.