Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 16
... draw a line and make it equal to a given line , these two lines are said to be equal by Construction . - A + B , or A plus B , - A — B , or A minus B , The signs and are to be read plus and minus . means A with B added to it , or the ...
... draw a line and make it equal to a given line , these two lines are said to be equal by Construction . - A + B , or A plus B , - A — B , or A minus B , The signs and are to be read plus and minus . means A with B added to it , or the ...
Σελίδα 19
... drawn from a cer- tain point within the figure , are equal . 13. That point is called the CENTRE of the circle . Ө 14. A DIAMETER of a circle is a straight line drawn through the centre , and terminating on both sides in the cir ...
... drawn from a cer- tain point within the figure , are equal . 13. That point is called the CENTRE of the circle . Ө 14. A DIAMETER of a circle is a straight line drawn through the centre , and terminating on both sides in the cir ...
Σελίδα 21
... drawn from any one point to any other point . 2. That any terminated straight line may be 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 ...
... drawn from any one point to any other point . 2. That any terminated straight line may be 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 ...
Σελίδα 23
... draw the straight lines CA , CB ( Post . 1 ) . The triangle ABC , thus con- structed , shall be equilateral . = For ... drawn from the given point C , is equal to the given line AB ( Ax . 1 ) . PROP . III . PROB . From the greater ( [ 23 ]
... draw the straight lines CA , CB ( Post . 1 ) . The triangle ABC , thus con- structed , shall be equilateral . = For ... drawn from the given point C , is equal to the given line AB ( Ax . 1 ) . PROP . III . PROB . From the greater ( [ 23 ]
Σελίδα 24
... draw a straight line AD , equal to C ( Prop . 2 ) ; and from the centre A , with the interval AD , describe a 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 ...
... draw a straight line AD , equal to C ( Prop . 2 ) ; and from the centre A , with the interval AD , describe a 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 ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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'.
Σελίδα 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.
Σελίδα 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.
Σελίδα 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.