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

### Dentro del libro

Resultados 1-5 de 25

Página 16

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**difference**of A and B , or A with B taken from it . The sign of multiplication is X ; thus AX B signifies A multiplied by B. In speaking of rectangles , the adjacent sides are written with a point between them ; thus ABCD expresses the ... Página 25

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**differences**between the former and the latter will be equal ( Ax . 3 ) ; therefore BF = CG ; and , as has been already demon- strated , FC = GB , and the angles F and G contained by those equal sides are equal ; therefore the triangles ... Página 33

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**difference**between any two sides of a triangle is less than the third side . For the greater of those two sides is equal to the less side and the**difference**between them ; but , by this proposition , it is less than the less side and ... Página 34

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**difference**between DG and EF ( Prop . 20 ) , those circles cannot lie one within the other ; they must therefore intersect . Draw therefore to the point of intersection K , the lines DK , EK , and the triangle DKE thus described , will ... Página 73

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**difference**between ECB and ECA , that is to say , ACB , is double of the differ- ence between / ECG and ECF , or / FCG : and since s ECG , ECF are respectively equal to s EDB , EDA , their**differences**are also equal ( Ax . 3 ) , or ...### 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.