## 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

Resultados 1-5 de 100

Página vii

...

...

**THIRD**BOOK OF EUCLID . 1. In a given line , straight or curved , find a point from which , as centre , if a circle be described , it will pass through two given points . When will this be impossible , and when will there be more than ... Página 7

...

...

**third**, the construction ; and the fourth , the demonstration .. That is , to describe an equilateral triangle , which shall have given a straight line as one of its sides . The word finite is employed to show that the line is not of ... Página 9

...

...

**third**sides , † equal ; ( 2 ) the two triangles are equal ; and ( 3 ) their other angles are equal , each to each , viz . those to which the equal sides are opposite.§ Let ABC , DEF be two triangles which have the two sides AB , sition ... Página 10

...

...

**third**definition . Also B will coincide with E , because AB is equal to DE . If B fell between D and E , AB would be less than DE ; but if B fell on the continuation of DE through E , AB would be greater than DE . Again , the angles A ... Página 18

... . is also evident , that when AEC and BED have been proved to be equal , the equa- lity of AED and BEC might be inferred from the 13th proposition , and the

... . is also evident , that when AEC and BED have been proved to be equal , the equa- lity of AED and BEC might be inferred from the 13th proposition , and the

**third**axiom . PROP . XVI . THEOR . - If one side 18 [ BOOK L THE ELEMENTS.### 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.