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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Αποτελέσματα 1 - 5 από τα 88.
Σελίδα v
... prove acceptable to all lovers of accurate reasoning and of ma- thematical learning , to remove such blemishes , and restore the principal Books of the Elements to their original accuracy , as far as I was able ; especially since these ...
... prove acceptable to all lovers of accurate reasoning and of ma- thematical learning , to remove such blemishes , and restore the principal Books of the Elements to their original accuracy , as far as I was able ; especially since these ...
Σελίδα 6
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : but things which are equal to the same thing are * 1 Axiom . equal to one another ; therefore CA is equal to CB ; where- fore CA , AB , BC are equal to one ...
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : but things which are equal to the same thing are * 1 Axiom . equal to one another ; therefore CA is equal to CB ; where- fore CA , AB , BC are equal to one ...
Σελίδα 8
... proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B coin- ciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would ...
... proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B coin- ciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would ...
Σελίδα 9
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each and the angle BFC was proved to be equal to the angle CGB , and the base BC is com- mon to the two triangles BFC , CGB ; wherefore ...
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each and the angle BFC was proved to be equal to the angle CGB , and the base BC is com- mon to the two triangles BFC , CGB ; wherefore ...
Σελίδα 11
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 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.
Σελίδα 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Σελίδα 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...
Σελίδα 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.
Σελίδα 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Σελίδα 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.