## 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 33

Side 62

... Wherefore , if any two points , & c . Q.E.D. PROP . III . THEOR . * 1. 3 . If a straight line drawn through the centre of a circle bisect a straight line in it which does not

... Wherefore , if any two points , & c . Q.E.D. PROP . III . THEOR . * 1. 3 . If a straight line drawn through the centre of a circle bisect a straight line in it which does not

**pass**through the centre , it shall cut ... Side 63

If in a circle two straight lines cut one another which do not both

If in a circle two straight lines cut one another which do not both

**pass**through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not ... Side 69

If two circles touch each other internally , the straight line which joins their centres being produced shall

If two circles touch each other internally , the straight line which joins their centres being produced shall

**pass**through the point of contact . Let the two circles ABC , ADE touch each other internally in the point A , and let F be ... Side 70

But it is also lessa ; which is impossible : Therefore the straight line which joins the points F , G shall not

But it is also lessa ; which is impossible : Therefore the straight line which joins the points F , G shall not

**pass**otherwise than through the point of contact A , that is , it must**pass**through it . Therefore , if two circles , & c . Side 71

... EG , perpendiculars to AB , CD : Then , because the straight line EF , passing through the centre , cuts the straight line AB , which does not

... EG , perpendiculars to AB , CD : Then , because the straight line EF , passing through the centre , cuts the straight line AB , which does not

**pass**through the centre , at right angles , it also bisectsa it : Wherefore AF is A * 3.### 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.