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 |
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Αποτελέσματα 1 - 5 από τα 66.
Σελίδα 3-10
... square upon a given straight line . Let AB be the given straight line ; It is required to de- scribe a square upon AB . E From the point A drawa AC at right angles to AB ... AC the squares GB , HC ; and through A drawb AL 40 THE ELEMENTS.
... square upon a given straight line . Let AB be the given straight line ; It is required to de- scribe a square upon AB . E From the point A drawa AC at right angles to AB ... AC the squares GB , HC ; and through A drawb AL 40 THE ELEMENTS.
Σελίδα 3-11
Euclides Robert Simson. squares GB , HC ; and through A drawb AL parallel to BD , Book I. or CE , and join AD , FC . Then , because each of the angles BAC , BAG is a rightangle , the two straight lines AC , AG , upon the opposite sides ...
Euclides Robert Simson. squares GB , HC ; and through A drawb AL parallel to BD , Book I. or CE , and join AD , FC . Then , because each of the angles BAC , BAG is a rightangle , the two straight lines AC , AG , upon the opposite sides ...
Σελίδα 3-12
... AC , and make AD equal to BA , and join DC : Then , because DA is equal to AB , the square of DA is equal to the square of AB : To each of these add the square of AC ; therefore the squares of DA , AC are equal to the squares of BA , AC ...
... AC , and make AD equal to BA , and join DC : Then , because DA is equal to AB , the square of DA is equal to the square of AB : To each of these add the square of AC ; therefore the squares of DA , AC are equal to the squares of BA , AC ...
Σελίδα 3-14
... AC , shall be equal to the square of AB . B Upon AB describe the square 31. 1. ADEB , and through C drawb CF parallel to AD or BE . Then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and AF is the rectangle ...
... AC , shall be equal to the square of AB . B Upon AB describe the square 31. 1. ADEB , and through C drawb CF parallel to AD or BE . Then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and AF is the rectangle ...
Σελίδα 3-15
... square of the aforesaid part . Let the straight line AB be divided into two parts in the point C ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of BC . Upon BC describe the square A C CDEB , and ...
... square of the aforesaid part . Let the straight line AB be divided into two parts in the point C ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of BC . Upon BC describe the square A C CDEB , and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 16 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.