## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |

### Dentro del libro

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Página 22

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**coincide**with one another ( that is to say , which fit together so exactly that every point of the one lies on some point of the other ) are equal . 9. The whole is greater than its part . 10. All right angles are equal to one another ... Página 24

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**coincide**with F , and the side CA may fall on FD which is equal to it , and that the other pair of equal sides may lie at the same side of those which fall together . D Then since CA and FD falling together ,**coincide**at their ... Página 25

Euclides William Desborough Cooley.

Euclides William Desborough Cooley.

**coincide**, and also the equal sides , it is evident that the angles contained by or opposite to equal sides , must be equal , and that the triangles themselves are equal in every respect ( Ax . 8 ) ... Página 27

... the extremity A of the base of the one may

... the extremity A of the base of the one may

**coincide**with that extremity D of the base of the other , at which terminates the side DF equal to AC ; and that AB may fall A C F B on DE , and the triangles ACB , DFE may BOOK I. PROP . VIII . Página 28

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**coincide**, and therefore the bases themselves shall wholly**coincide**( Def . 3 ) . The two triangles ACB , DFE stand therefore on the same base , and on the same side of it , and their conterminous sides being equal they must**coincide**...### 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.