The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 9
... less than " two right angles , these straight lines being continually pro- " duced , shall at length meet upon that side on which are the angles " which are less than two right angles . See the notes on prop . " 29. of Book I. " 2 2 ...
... less than " two right angles , these straight lines being continually pro- " duced , shall at length meet upon that side on which are the angles " which are less than two right angles . See the notes on prop . " 29. of Book I. " 2 2 ...
Página 11
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
Página 13
... less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
... less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
Página 20
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A C Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) than the ...
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A C Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) than the ...
Página 21
... less than it ; it is not equal , because then the angle ABC would be equal ( 5. 1. ) to the an- gle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; be- cause then the angle ABC would be less ( 18. 1. ) than ...
... less than it ; it is not equal , because then the angle ABC would be equal ( 5. 1. ) to the an- gle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; be- cause then the angle ABC would be less ( 18. 1. ) than ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone 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 gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - 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.
Página 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 246 - 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 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 119 - 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 19 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Página 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.