## 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

Resultat 1-5 av 100

Side 7

Because the point A is the centre of the circle BCD , AC is

Because the point A is the centre of the circle BCD , AC is

**equal**to AB ; and because the point B is the centre < 15 Definiof the circle ACE , BC is**equal**to BA : But it has been tion . proved that CA is**equal**to AB ; therefore CA ... Side 8

Because the point B is the centre of the circle CGH , BC is equale to BG ; and because D is the centre of the e 15 Def . circle GKL , DL is

Because the point B is the centre of the circle CGH , BC is equale to BG ; and because D is the centre of the e 15 Def . circle GKL , DL is

**equal**to DG , and DA , DB , parts of them , are**equal**; therefore the remainder AL is**equal**to ... Side 9

AB to DE , and AC to Book I. DF ; and the angle BAC D

AB to DE , and AC to Book I. DF ; and the angle BAC D

**equal**to the angle EDF , the base BC shall be**equal**to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the**equal**sides B CE are opposite ... Side 10

Boox l .

Boox l .

**equal**to AC , and let the straight lines AB , AC be produced to D and E , the angle ABC shall be**equal**to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut * 3. Side 11

Let ABC be a triangle having the angle ABC

Let ABC be a triangle having the angle ABC

**equal**to Boox l . the angle ACB ; the side AB is also**equal**to the side AC . For , if AB be not**equal**to AC , one of them is greater than the other : Let AB be the greater ; and from it cut a ...### 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 arch 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 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 45 - 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 312 - 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 155 - 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 54 - 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 167 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.