## The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso |

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Page 8

... equal to one another , they shall also have

... equal to one another , they shall also have

**their**bases , or third sides , equal , and the two triangles shall be equal , and**their**other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Page 11

Q.E.D. COR . Hence every equiangular triangle is also equilateral . D PROP . VII . THEOR . Upon the same ase , and on the same side of it , there cannot be two triangles which have

Q.E.D. COR . Hence every equiangular triangle is also equilateral . D PROP . VII . THEOR . Upon the same ase , and on the same side of it , there cannot be two triangles which have

**their**sides terminated in ... Page 12

If two triangles have two sides of the one equal to two sides of the other , each to each , and have also

If two triangles have two sides of the one equal to two sides of the other , each to each , and have also

**their**bases equal , the angle which is contained by the two sides of the one shall be equal to the angle contained by the two ... Page 13

... and upon the same side of it , there would be two triangles having

... and upon the same side of it , there would be two triangles having

**their**sides terminated in one extremity of the base equal to one another , and also those terminated in the other extremitywhich is impossible ( 1. Page 35

26 )

26 )

**their**other sides are equal , each to each , and the third angle of the one to the third angle of the other viz . the side AB to the side CD , and AC to BD , and the angle BAC to the angle BDC : Then because the angle ABC is equal ...### What people are saying - Write a review

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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |

### Common terms and phrases

ABCD angle ABC angle ACB angle BAC base base BC BC is equal bisected centre chord circle circle ABC circumference common described diameter difference divided double draw drawn equal equal angles equiangular equimultiples extremities fall figure fore four fourth given circle given line given point given straight line greater half inscribed intersection join less Let ABC lines be drawn lines drawn magnitudes manner meet multiple opposite sides parallel parallelogram pass perpendicular plane polygon PROB produced PROP proportionals Q.E.D. PROP rectangle rectangle contained rectilineal figure right angles segment semicircle shew shewn sides similar square square of AC straight lines &c Take taken THEOR third touches the circle triangle ABC Wherefore whole

### Popular passages

Page 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 4 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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.

Page 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 22 - If from the ends of a 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.

Page 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.

Page 194 - 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.

Page 2 - 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 : 16.

Page 69 - 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.