## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 páginas |

### Dentro del libro

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Página 46

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**difference**of the squares of two unequal lines AC , CD , is equal to the rect- angle contained by their sum AD and**difference**DB . PROP . VI . THEOR . If a straight line 46 THE ELEMENTS. Página 288

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**difference**of the other two : From this , he shows that the circles must meet one another , in one case ; and says , that it may be proved DM FG after the same manner in any other case : But the straight H line GM which he bids take ... Página 301

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**difference**between the two de- monstrations , except a single word in the construction , which very probably has been owing to an unskilful librarian . Clavius B G C F D Book V. likewise gives both the ways ; but neither NOTES . 301. Página 315

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**difference**betwixt this compound- " ing of ratios , and the duplication or triplication of them " which are defined in the 5th Book , but that in the duplica- ❝tion , triplication , & c . of ratios , all the interposed ratios are equal ... Página 324

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**difference**of the sides of a rectangle , and the magnitude of it , to find the sides . PROP . XXXI . B. VI . In the demonstration of this , the inversion of proportionals is twice neglected , and is now added , that the conclusion may ...### Otras ediciones - Ver todas

### Términos y frases comunes

ABC is given altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABCD circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore

### Pasajes populares

Página 47 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.

Página 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Página 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Página 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Página 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.

Página 153 - 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 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...

Página 28 - 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 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.

Página 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...