Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Seite 19
... circle . Ө 14. A DIAMETER of a circle is a straight line drawn through the centre , and terminating on both sides in the cir- cumference . 15. A SEMICIRCLE is the figure contained by the diameter and the part of the circle cut off by ...
... circle . Ө 14. A DIAMETER of a circle is a straight line drawn through the centre , and terminating on both sides in the cir- cumference . 15. A SEMICIRCLE is the figure contained by the diameter and the part of the circle cut off by ...
Seite 21
... circle may be described from any centre , with any interval from that centre . AXIOMS . 1. Things which are equal to the same thing , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be ...
... circle may be described from any centre , with any interval from that centre . AXIOMS . 1. Things which are equal to the same thing , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be ...
Seite 23
... circle BCD ( Post . 3 ) ; and again , from B as centre , with the interval BA , describe the circle ACE ; and from the point C , in which these circles intersect each other , draw the straight lines CA , CB ( Post . 1 ) . The triangle ...
... circle BCD ( Post . 3 ) ; and again , from B as centre , with the interval BA , describe the circle ACE ; and from the point C , in which these circles intersect each other , draw the straight lines CA , CB ( Post . 1 ) . The triangle ...
Seite 24
... circle ( Post . 3 ) . The part AE cut off from AB by this circle towards its centre , shall be equal to C. = For AE AD ( Def . 12 ) ; and AD = C ( Const . ) ; therefore AE , the part cut off from the greater line AB , is equal to the ...
... circle ( Post . 3 ) . The part AE cut off from AB by this circle towards its centre , shall be equal to C. = For AE AD ( Def . 12 ) ; and AD = C ( Const . ) ; therefore AE , the part cut off from the greater line AB , is equal to the ...
Seite 29
... circle , cutting AB in E and F. Bisect EF in D ( Prop . 10 ) , and draw CD . This line CD shall be perpendicular to AB . A E P For draw CE and CF ; and since the triangles CED , CFD have CD common to both , and the sides CE = CF ( Def ...
... circle , cutting AB in E and F. Bisect EF in D ( Prop . 10 ) , and draw CD . This line CD shall be perpendicular to AB . A E P For draw CE and CF ; and since the triangles CED , CFD have CD common to both , and the sides CE = CF ( Def ...
Häufige Begriffe und Wortgruppen
ACDB adjacent angles angles equal antecedent Axioms base bisected centre chord circumference coincide consequently Const definition demonstrated describe diagonal diameter difference divided draw equal angles equal Prop equal sides equiangular equilateral triangle equimultiples Euclid Euclid's Elements external angle extremities fore fourth fractional Geometry given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed internal intersect isosceles triangle less line drawn lines be drawn magnitudes manner meeting multiple opposite angles parallel parallelogram perpendicular point of contact PROB produced proportional Proposition quadrilateral figure rectangle contained rectilinear figure remaining angles respectively equal right angle segment semiperimeter sides AC sides equal square of half subtending taken tangent THEOR third triangles ABC unequal vertex whole line
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Seite 126 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 155 - 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.
Seite 83 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Seite 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Seite 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 90 - BFE : (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.
Seite 117 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Seite 56 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Seite 60 - Iff 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.
Seite 78 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.