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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Side 72
... ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the cen- tre than FG ; AD is greater than any straight line BC , which is not a dia- meter , and BC greater than FG . From the centre draw EH ...
... ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the cen- tre than FG ; AD is greater than any straight line BC , which is not a dia- meter , and BC greater than FG . From the centre draw EH ...
Side 75
... circle . Find a the centre E of the circle , and join AE ; and from * 1. 3 . the centre E , at the distance EA ... ABC in the point C ; take the centre F , and draw the straight line FC : FC is perpendicular to DE . For , if it be not ...
... circle . Find a the centre E of the circle , and join AE ; and from * 1. 3 . the centre E , at the distance EA ... ABC in the point C ; take the centre F , and draw the straight line FC : FC is perpendicular to DE . For , if it be not ...
Side 76
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the ... circumference . Let ABC be a circle , and BEC an angle 76 THE ELEMENTS.
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the ... circumference . Let ABC be a circle , and BEC an angle 76 THE ELEMENTS.
Side 77
Euclides Robert Simson. Let ABC be a circle , and BEC an angle at the centre , Boox III . and BAC an angle at the circumference , which have them same circumference BC for their base ; the angle BEC is double of the angle BAC . 5. 1 . E ...
Euclides Robert Simson. Let ABC be a circle , and BEC an angle at the centre , Boox III . and BAC an angle at the circumference , which have them same circumference BC for their base ; the angle BEC is double of the angle BAC . 5. 1 . E ...
Side 78
... circle , let BAD , BED be angles in it ; these also are equal to one ano- ther : Draw AF to the centre , and produce ... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right ...
... circle , let BAD , BED be angles in it ; these also are equal to one ano- ther : Draw AF to the centre , and produce ... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 16 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.