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 |
No interior do livro
Resultados 1-5 de 100
Página 8
... shown , 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 . Wherefore from the given point A a ...
... shown , 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 . Wherefore from the given point A a ...
Página 20
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. b 18. 1 . PROP . XX . THEOR . See N. ANY two sides of a triangle are together greater than the third side . Let ABC be a ...
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. b 18. 1 . PROP . XX . THEOR . See N. ANY two sides of a triangle are together greater than the third side . Let ABC be a ...
Página 21
... shown that BA , AC are greater than BE , B A E D EC , much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
... shown that BA , AC are greater than BE , B A E D EC , much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
Página 24
... shown that it is not equal to it ; there- fore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . Ir two triangles have two angles of one equal to two angles of the other ...
... shown that it is not equal to it ; there- fore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . Ir two triangles have two angles of one equal to two angles of the other ...
Página 29
... shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
... shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
Outras edições - Ver tudo
The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Visualização integral - 1834 |
Palavras e frases frequentes
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
Passagens conhecidas
Página 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.
Página 16 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.