Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Página 59
... touch a circle when it meets , and being produced , does not cut the circle . 4. Circles are said to touch one another which meet but do no cut one an- other . 5. Straight lines are said to be equally distant from the centre of a circle ...
... touch a circle when it meets , and being produced , does not cut the circle . 4. Circles are said to touch one another which meet but do no cut one an- other . 5. Straight lines are said to be equally distant from the centre of a circle ...
Página 63
... touch internally , they have not the same centre . 1 F D K For suppose it possible that the two circles , the one touch- ing the other internally at the point F , have the common centre C. Join CF , and also draw CB , meeting the ...
... touch internally , they have not the same centre . 1 F D K For suppose it possible that the two circles , the one touch- ing the other internally at the point F , have the common centre C. Join CF , and also draw CB , meeting the ...
Página 66
... touch each other in the point D , then from C , the centre of the circle AED , draw the lines CA , CB , CD , and these lines are equal ( i . Def . 12 ) ; but since from the point C more than two straight lines are drawn to the ...
... touch each other in the point D , then from C , the centre of the circle AED , draw the lines CA , CB , CD , and these lines are equal ( i . Def . 12 ) ; but since from the point C more than two straight lines are drawn to the ...
Página 67
... touch each other internally , the straight line joining their centres will , when produced , pass through a point of contact ( A ) . E B A G D For , if it be supposed that G and F are the centres of the circles , and that the straight ...
... touch each other internally , the straight line joining their centres will , when produced , pass through a point of contact ( A ) . E B A G D For , if it be supposed that G and F are the centres of the circles , and that the straight ...
Página 68
... touch each other either internally or externally in more than one point . First , in the case of internal contact , the line AB joining the centres of the circles , must pass through a point of contact C ( iij . Prop . 11 ) ; and if it ...
... touch each other either internally or externally in more than one point . First , in the case of internal contact , the line AB joining the centres of the circles , must pass through a point of contact C ( iij . Prop . 11 ) ; and if it ...
Términos y frases comunes
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
Pasajes populares
Página 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'.
Página 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.
Página 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.
Página 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.