## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 páginas |

### Dentro del libro

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Página vii

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**corollary**to the fifth . The next should be done by means of the twelfth and thirteenth propositions , and the same**corollary**, cutting it , and if the parts of one of EASY EXERCISES . vii. Página xi

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**corollary**is an inference which arises easily and immediately from some other principle , not requiring any lengthened process of reasoning to establish its truth . The truth of this**corollary**is manifest , since , from the definition ... Página 4

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**corollaries**are established , we are no more entitled to conclude that a quadri- lateral can have four right angles than that it can have four obtuse or four acute ones . The definition above quoted , however , has the advantage of ... Página 5

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**corollary**, as already ex- plained , is likewise a proposition . It may also be remarked that a proposition which is preparatory to one or more others , and which is of no other use , is called a lemma . Such a proposition is thrown ... Página 13

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**corollaries**to the 3d and 5th definitions . * This proposition is merely a lemma to the 8th , and may be omitted , if the second method of demonstrating that proposition be adopted . PROP . VIII . THEOR . - If two triangles BOOK I. ] 13 ...### Otras ediciones - Ver todas

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Sin vista previa disponible - 2016 |

### Términos y frases comunes

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore

### Pasajes populares

Página 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Página 45 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Página 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Página 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Página 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Página 7 - If two triangles have two sides of the one equal to two sides of the...

Página 27 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Página 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Página 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Página 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.