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].1814 |
From inside the book
Results 1-5 of 100
Page 31
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diame- ter ; the opposite sides and angles of the figure are equal to one another ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diame- ter ; the opposite sides and angles of the figure are equal to one another ...
Page 32
... parallelogram ACDB into two equal parts . 4. 1. Q. E. D. PROP . XXXV . THEOR . See N. PARALLELOGRAMS upon the same base , and be- tween the same parallels , are equal to one another . See the 2d Let the parallelograms ABCD , EBCF be ...
... parallelogram ACDB into two equal parts . 4. 1. Q. E. D. PROP . XXXV . THEOR . See N. PARALLELOGRAMS upon the same base , and be- tween the same parallels , are equal to one another . See the 2d Let the parallelograms ABCD , EBCF be ...
Page 33
... parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E.D. с 35. 1 . PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
... parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E.D. с 35. 1 . PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
Page 33
... parallelogram DBCF , because the diameter DC bi- sects it : but the halves of equal things are equald ; there- fore ... parallelogram ; and they are equal 36. 1. tob one another , be- H cause they are upon equal bases BC , B CE EF , and ...
... parallelogram DBCF , because the diameter DC bi- sects it : but the halves of equal things are equald ; there- fore ... parallelogram ; and they are equal 36. 1. tob one another , be- H cause they are upon equal bases BC , B CE EF , and ...
Page 33
... parallelogram and triangle be upon the same base , and between the same parallels ; the paral- lelogram shall be double of the triangle . BOOK I. Let the parallelogram ABCD and the triangle EBC D 2 OF EUCLID . 35.
... parallelogram and triangle be upon the same base , and between the same parallels ; the paral- lelogram shall be double of the triangle . BOOK I. Let the parallelogram ABCD and the triangle EBC D 2 OF EUCLID . 35.
Other editions - View all
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 3-7 - 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.
Page 16 - Any two sides of a triangle are together greater than the third side.
Page 26 - 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 16 - 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...
Page 304 - 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.
Page 4 - 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.
Page 147 - 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 3-16 - 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.
Page 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.