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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 100.
Σελίδα xii
... manner of the ancients . He has only two pieces printed in the vo- lumes of the Philosophical Transactions : viz . of 1. Two general Propositions of Pappus , in which many Euclid's Porisms are included , vol . 32 , ann . 1723. — These ...
... manner of the ancients . He has only two pieces printed in the vo- lumes of the Philosophical Transactions : viz . of 1. Two general Propositions of Pappus , in which many Euclid's Porisms are included , vol . 32 , ann . 1723. — These ...
Σελίδα 13
... manner , because ABD is a straight line , the angle DBE is equal to the angle EBA ; wherefore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible : therefore , two straight lines cannot have a common ...
... manner , because ABD is a straight line , the angle DBE is equal to the angle EBA ; wherefore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible : therefore , two straight lines cannot have a common ...
Σελίδα 15
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which , therefore , is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. * PROPOSITION XV . THEOR If two ...
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which , therefore , is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. * PROPOSITION XV . THEOR If two ...
Σελίδα 16
... manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the ...
... manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the ...
Σελίδα 17
... manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. * PROPOSITION XVIII . THEOR . - The greater side of every triangle is opposite to the ...
... manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. * PROPOSITION XVIII . THEOR . - The greater side of every triangle is opposite to the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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.