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 30
Side 96
... PROPORTIONAL between the other two . [ In the analogy A : B :: B : C , B is a mean proportional between C and D. ] 10. Of any number of magnitudes of the same kind , the first is said to have to the last a ratio compounded of the ratio ...
... PROPORTIONAL between the other two . [ In the analogy A : B :: B : C , B is a mean proportional between C and D. ] 10. Of any number of magnitudes of the same kind , the first is said to have to the last a ratio compounded of the ratio ...
Side 102
... proportional . PROP . C. THEOR . If the first be to the second as the third to the fourth , and if the first be a multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A : B :: C : D ...
... proportional . PROP . C. THEOR . If the first be to the second as the third to the fourth , and if the first be a multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A : B :: C : D ...
Side 113
... proportional . 2. Two sides of one figure are said to be reciprocally pro- portional to two sides of another figure , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to ...
... proportional . 2. Two sides of one figure are said to be reciprocally pro- portional to two sides of another figure , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to ...
Side 114
... proportional to them ( v . Prop . 15 ) , or CKAB : EALD :: CAB : EAD ; but CAB : EAD :: CB : ED ; and therefore CKAB : EALD :: CB : ED ( v . Prop . 11 ) . COR . - Hence it is manifest that triangles and parallelo- grams , having equal ...
... proportional to them ( v . Prop . 15 ) , or CKAB : EALD :: CAB : EAD ; but CAB : EAD :: CB : ED ; and therefore CKAB : EALD :: CB : ED ( v . Prop . 11 ) . COR . - Hence it is manifest that triangles and parallelo- grams , having equal ...
Side 115
... proportional to the other sides of the triangle ( BD : DC :: BA : AC ) ; or , if the segments of the base be proportional to the other sides of the triangle , the straight line ( AD ) drawn from the vertex to the point of section ...
... proportional to the other sides of the triangle ( BD : DC :: BA : AC ) ; or , if the segments of the base be proportional to the other sides of the triangle , the straight line ( AD ) drawn from the vertex to the point of section ...
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.