## The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |

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Resultat 1-5 av 5

Side 71

For the same

AF is equal to CG : And because AE is equal ... 1 . the square of AE , because the

angle AFE is a right angle ; and for the like

For the same

**reason**CD is double of CG : And AB is equal to CD ; there - F foreAF is equal to CG : And because AE is equal ... 1 . the square of AE , because the

angle AFE is a right angle ; and for the like

**reason**, the squares of EG , GC are ... Side 104

3 . angle BAE is equalf to the angle AED : For the same

angles ABC , BCD , CDE is equal to the angle BAE , or AED : Therefore the

pentagon ABCDE is equiangular ; and it has been shown that it is equilateral .

Wherefore ...

3 . angle BAE is equalf to the angle AED : For the same

**reason**, cach of theangles ABC , BCD , CDE is equal to the angle BAE , or AED : Therefore the

pentagon ABCDE is equiangular ; and it has been shown that it is equilateral .

Wherefore ...

Side 169

For the same

therefore the similar polygons ABCDE , FGHKL are divided into the same number

of similar triangles . Also these triangles have , each to each , the same ratio ...

For the same

**reason**, the triangle ECD likewise is similar to the triangle LHK :therefore the similar polygons ABCDE , FGHKL are divided into the same number

of similar triangles . Also these triangles have , each to each , the same ratio ...

Side 250

Book XII . equal to the base KD , and the triangle AEH equals and similar to the

triangle HKD ; For the same

triangle HLD : And because the two straight lines EH , HG , which meet one ...

Book XII . equal to the base KD , and the triangle AEH equals and similar to the

triangle HKD ; For the same

**reason**, the triangle AGH is equal and similar to thetriangle HLD : And because the two straight lines EH , HG , which meet one ...

Side 301

account another construction and demonstration is given , Book III , which is the

same with the second part of that which Campanus has translated from the

Arabic , where , without any

account another construction and demonstration is given , Book III , which is the

same with the second part of that which Campanus has translated from the

Arabic , where , without any

**reason**, the denionstration is divided into two parts .### Hva folk mener - Skriv en omtale

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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 43 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 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.

Side 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.

Side 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.

Side 52 - 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 of the other part.

Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Side 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.