## 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 104

It is also

circumference DE : If to each be added BCD , the whole ABCD is equal to the

whole EDCB : And the angle AED stands on the circumference ABCD , and the

angle BAE on ...

It is also

**equiangular**; because the circumference AB is equal to thecircumference DE : If to each be added BCD , the whole ABCD is equal to the

whole EDCB : And the angle AED stands on the circumference ABCD , and the

angle BAE on ...

Side 109

To inscribe an equilateral and

circle . Let ABCD be the given circle ; it is required to inscribe an equilateral and

equilateral ...

To inscribe an equilateral and

**equiangular**quin - See N . decagon in a givencircle . Let ABCD be the given circle ; it is required to inscribe an equilateral and

**equiangular**quindecagon in the circle ABCD . Let AC be the side of anequilateral ...

Side 157

Therefore the angles ABC , DEF are not unequal , that is , they are equal ; And

the angle at A is equal to the angle at D ; wherefore the remaining angle at C is

equal to the remaining angle at F : Therefore the triangle ABC is

the ...

Therefore the angles ABC , DEF are not unequal , that is , they are equal ; And

the angle at A is equal to the angle at D ; wherefore the remaining angle at C is

equal to the remaining angle at F : Therefore the triangle ABC is

**equiangular**tothe ...

Side 166

6 . the triangles GAB , FCD being

because AG is to GB , as CF to FD ; and as GB to GH , so , by reason of the

AG is to ...

6 . the triangles GAB , FCD being

**equiangular**, BA is to AG , as DC to CF ; andbecause AG is to GB , as CF to FD ; and as GB to GH , so , by reason of the

**equiangular**trid 22 . 5 . angles BGH , DFE , is FD to FE ; therefore , ex æqualių ,AG is to ...

Side 411

E of BL to EG is given : and because BL is

hypothesis , the ratio of BC to FG is given ; i therefore the ratio of KB to EF $ 65

Dat AK DL : is given , and the ratio of KB to BA is given ; the ratio there- fored of

AB to ...

E of BL to EG is given : and because BL is

**equiangular**to . EG , and , by thehypothesis , the ratio of BC to FG is given ; i therefore the ratio of KB to EF $ 65

Dat AK DL : is given , and the ratio of KB to BA is given ; the ratio there- fored of

AB to ...

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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.