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
Page 479
... radius to the sine of BAD , which is the complement of the angle ABC ; that is , as radius to the cosine of ABC . PROP . VI . FIG . 11 .. IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half ...
... radius to the sine of BAD , which is the complement of the angle ABC ; that is , as radius to the cosine of ABC . PROP . VI . FIG . 11 .. IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half ...
Page 480
... radius is to the square of the tangent of the angle DAG , that is , the half of BAC : But HA is half the perimeter of the triangle ABC , and AD is the excess of the same above HD , that is , above the base BC ; but BF or CL is the ...
... radius is to the square of the tangent of the angle DAG , that is , the half of BAC : But HA is half the perimeter of the triangle ABC , and AD is the excess of the same above HD , that is , above the base BC ; but BF or CL is the ...
Page 481
... Radius ; T. for Tangent ; and S. for Sine . Degrees , minutes , seconds , & c . are written in this manner : 30 ° 25 ′ 13 ′′ , & c , which signifies 30 degrees , 25 minutes , 13 seconds , & c . Fig . 15 , Solution of the Cases of Right ...
... Radius ; T. for Tangent ; and S. for Sine . Degrees , minutes , seconds , & c . are written in this manner : 30 ° 25 ′ 13 ′′ , & c , which signifies 30 degrees , 25 minutes , 13 seconds , & c . Fig . 15 , Solution of the Cases of Right ...
Page 485
... radius , which is supposed unity ; and is con- ceived to be divided into 10000000 or more decimal parts . And so the sine , tangent , or secant of an arc , may be had by help of this table ; and , contrariwise , a sine , tangent , or ...
... radius , which is supposed unity ; and is con- ceived to be divided into 10000000 or more decimal parts . And so the sine , tangent , or secant of an arc , may be had by help of this table ; and , contrariwise , a sine , tangent , or ...
Page 486
... radius . Therefore DE , EB , being given , in the right angled triangle DBE , there will be given DB , whose half DM is the sine of the arc DL the are BD . PROP . IV . PROB . Fig . 29. THE sine BM of the arc BL being given , to find the ...
... radius . Therefore DE , EB , being given , in the right angled triangle DBE , there will be given DB , whose half DM is the sine of the arc DL the are BD . PROP . IV . PROB . Fig . 29. THE sine BM of the arc BL being given , to find the ...
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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.