The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
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Page 386
... Sine of the arch AC , or of the angle ABC , of which it is the measure . COR . The Sine of a quadrant , or of a right angle , is equal to the radius . V. The segment DA of the diameter passing through A , one extremity of the arch AC ...
... Sine of the arch AC , or of the angle ABC , of which it is the measure . COR . The Sine of a quadrant , or of a right angle , is equal to the radius . V. The segment DA of the diameter passing through A , one extremity of the arch AC ...
Page 387
... sine , versed sine , tangent , and secant , of any angle , may be found in parts of which the radius contains a given number ; and , vice versa , a number expressing the length of the sine , versed sine , tangent , and secant , being ...
... sine , versed sine , tangent , and secant , of any angle , may be found in parts of which the radius contains a given number ; and , vice versa , a number expressing the length of the sine , versed sine , tangent , and secant , being ...
Page 388
... sine of the angle CBA , and BD the sine of the angle ACB : but the two triangles CAE , DAB have each a right angle at D and E ; and likewise the common angle CAB ; therefore they are similar , and consequently , CA is to AB as CE to DB ...
... sine of the angle CBA , and BD the sine of the angle ACB : but the two triangles CAE , DAB have each a right angle at D and E ; and likewise the common angle CAB ; therefore they are similar , and consequently , CA is to AB as CE to DB ...
Page 389
... sine of the angle included by the two sides . Let ABC be a plane triangle ; twice the rectangle ABC contained by any two sides BA , BC , is to the difference of the sum of the squares of BA , BC , and the square of the base AC , as the ...
... sine of the angle included by the two sides . Let ABC be a plane triangle ; twice the rectangle ABC contained by any two sides BA , BC , is to the difference of the sum of the squares of BA , BC , and the square of the base AC , as the ...
Page 392
... Sine . Degrees , minutes , seconds , & c . are written in this manner ; 30 ° 25 ′ 13 " , & c . , which signifies 30 degrees , 25 minutes , 13 seconds , & c . SOLUTION OF THE CASES OF RIGHT ANGLED TRIANGLES . GENERAL 392 PLANE TRIGONOMETRY .
... Sine . Degrees , minutes , seconds , & c . are written in this manner ; 30 ° 25 ′ 13 " , & c . , which signifies 30 degrees , 25 minutes , 13 seconds , & c . SOLUTION OF THE CASES OF RIGHT ANGLED TRIANGLES . GENERAL 392 PLANE TRIGONOMETRY .
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Page 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Page 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Page 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 256 - 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 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Page 20 - ANY two angles of a triangle are together less than two right angles.