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 17
... opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . Because the straight line AE makes with CD the angles CEA , AED ...
... opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . Because the straight line AE makes with CD the angles CEA , AED ...
Side 18
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . * 10. 1 . Bisecta AC in E , join BE and produce it to F , A and ...
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . * 10. 1 . Bisecta AC in E , join BE and produce it to F , A and ...
Side 19
... opposite to the greater angle . BOOK I. 13. 1 . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle A ABC is also greater than the angle BCA . Because AC is greater than AB , makea AD equal to AB , В and ...
... opposite to the greater angle . BOOK I. 13. 1 . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle A ABC is also greater than the angle BCA . Because AC is greater than AB , makea AD equal to AB , В and ...
Side 21
... opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the ...
... opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the ...
Side 24
... opposite to equal angles in each ; then shall the other sides be equal , each to each : and also the third angle of the one to the third angle of the other . Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the ...
... opposite to equal angles in each ; then shall the other sides be equal , each to each : and also the third angle of the one to the third angle of the other . Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the ...
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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 arch base BC bisected Book XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawa 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 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 triangle ABC versed sine vertex wherefore
Populære avsnitt
Side 45 - 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 20 - Any two sides of a triangle are together greater than the third side.
Side 30 - 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 20 - 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 312 - 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 8 - 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 155 - 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 54 - 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 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Side 167 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.