Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
Inni boken
Resultat 1-5 av 58
Side 18
... produced ( or continued ) beyond its vertex , the angles made by them on both sides of the vertex are said to be vertically opposite to each other thus , since GC is continued to D , and EC to F , the angles GCE and DCF are vertically ...
... produced ( or continued ) beyond its vertex , the angles made by them on both sides of the vertex are said to be vertically opposite to each other thus , since GC is continued to D , and EC to F , the angles GCE and DCF are vertically ...
Side 19
... produced . 11. A FIGURE is that which is enclosed by one or more boundaries . [ The space enclosed within a figure is called its AREA . ] 12. A CIRCLE is a plane figure bounded by one line called the CIRCUMFERENCE or periphery ; to ...
... produced . 11. A FIGURE is that which is enclosed by one or more boundaries . [ The space enclosed within a figure is called its AREA . ] 12. A CIRCLE is a plane figure bounded by one line called the CIRCUMFERENCE or periphery ; to ...
Side 20
... produced , the angle made by the produced part , with the other leg of the angle , from the vertex of which it was produced , is called an external angle ; and the angle of the triangle having the same vertex with it , is the internal ...
... produced , the angle made by the produced part , with the other leg of the angle , from the vertex of which it was produced , is called an external angle ; and the angle of the triangle having the same vertex with it , is the internal ...
Side 21
... produced or continued to any length in a straight line . 3. That a 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 ...
... produced or continued to any length in a straight line . 3. That a 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 ...
Side 23
... produce DC to its circumference L : the produced part CL shall be the line required . D C L B F For DL = DF ( Def . 12 ) , and DC = DB ( Const . ) ; and if the latter be taken from the former , there will remain CL = BF ( Ax . 3 ) ; but ...
... produce DC to its circumference L : the produced part CL shall be the line required . D C L B F For DL = DF ( Def . 12 ) , and DC = DB ( Const . ) ; and if the latter be taken from the former , there will remain CL = BF ( Ax . 3 ) ; but ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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'.
Side 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.
Side 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.
Side 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Side 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.