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].1834 |
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Página 8
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to ...
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to ...
Página 9
... equal tot AG , and AB to AC , the two + Constr . sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is equal * to the * 4. 1 . base ...
... equal tot AG , and AB to AC , the two + Constr . sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is equal * to the * 4. 1 . base ...
Página 12
... angle ; that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is required to bisect it . * Take any point D in AB , and from AC , cut * off AE equal to AD ; join DE , and upon it describe an ...
... angle ; that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is required to bisect it . * Take any point D in AB , and from AC , cut * off AE equal to AD ; join DE , and upon it describe an ...
Página 14
... angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two angles DBE , EBA , add to each of these equals the angle ABC ; therefore the angles * 1 Ax . DBA , ABC are equal to. 14 ...
... angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two angles DBE , EBA , add to each of these equals the angle ABC ; therefore the angles * 1 Ax . DBA , ABC are equal to. 14 ...
Página 16
... angles ; wherefore the angles CEA , AED are equal to the angles AED ; DEB : take away the common angle AED , and the re- maining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated , that the angles CEB ...
... angles ; wherefore the angles CEA , AED are equal to the angles AED ; DEB : take away the common angle AED , and the re- maining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated , that the angles CEB ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Visualização integral - 1814 |
Palavras e frases frequentes
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circle EFGH circumference common logarithm cone Constr 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 gnomon greater join less Let ABC logarithm multiple parallel parallelogram perpendicular point F polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR.-If tiple triangle ABC vertex wherefore
Passagens conhecidas
Página 32 - To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle...
Página 138 - 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 39 - 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.
Página 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 41 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Página 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...
Página 262 - 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 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Página 165 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.