## 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]. |

### Inni boken

Side 10

1 . equalb to the base GB , and the triangle AFC to the triangle AGB ; and the

each to each , ' to which the equal sides are opposite ; viz , the angle ACF to the ...

1 . equalb to the base GB , and the triangle AFC to the triangle AGB ; and the

**remaining**angies of the one are equal b to the**remaining**angles of the other ,each to each , ' to which the equal sides are opposite ; viz , the angle ACF to the ...

Side 144

... of any of the last ; then the ratio compounded of the

or the

compounded of those rernaining of the last , or with the

.

... of any of the last ; then the ratio compounded of the

**remaining**ratios of the first ,or the

**remaining**ratio of the first , if but one remain , is the same with the ratiocompounded of those rernaining of the last , or with the

**remaining**ratio of the last.

Side 155

At the points D , F , in the straight line DF , make a the• 23 , 1 . angle FDG equal to

either of the angles BAC , EDF ; and the angle DFG equal to the angle ACB :

Wherefore the

.

At the points D , F , in the straight line DF , make a the• 23 , 1 . angle FDG equal to

either of the angles BAC , EDF ; and the angle DFG equal to the angle ACB :

Wherefore the

**remaining**angle at B is equal to the**remaining**one at Gb , and 632.

Side 156

See N . If two triangles have one angle of the one equal to one angle of the other

, and the sides about two other angles proportionals , then , if each of the

be a ...

See N . If two triangles have one angle of the one equal to one angle of the other

, and the sides about two other angles proportionals , then , if each of the

**remaining**angles be either less , or not less , than a right angle ; or if one of thembe a ...

Side 236

1 . wherefore the base BC is equalf to the base EF , and the

the

the right angle ABK is equal to the right angle DEN , whence the

...

1 . wherefore the base BC is equalf to the base EF , and the

**remaining**angles tothe

**remaining**angles : The angle ABC is therefore equal to the angle DEF : Andthe right angle ABK is equal to the right angle DEN , whence the

**remaining**angle...

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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.