The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthDesilver, Thomas & Company, 1838 - 416 Seiten |
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Seite 7
... which has three acute angles . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong , is that which has all BOOK I. THE ELEMENTS OF EUCLID .
... which has three acute angles . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong , is that which has all BOOK I. THE ELEMENTS OF EUCLID .
Seite 37
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the point ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the point ...
Seite 38
... square described upon the side BC is equal to the squares de- scribed upon BA , AC . F B G li 1 K On BC describe ( 46. 1. ) the square BDEC , and on BA , AC the squares GB , HC : and through A draw ( 31. 1. ) AL parallel to BD or CE ...
... square described upon the side BC is equal to the squares de- scribed upon BA , AC . F B G li 1 K On BC describe ( 46. 1. ) the square BDEC , and on BA , AC the squares GB , HC : and through A draw ( 31. 1. ) AL parallel to BD or CE ...
Seite 39
... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC are equal to the squares of BA , AC : but the square of DC is equal ( 47. 1. ) to the squares of DA , AC , because DAC ...
... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC are equal to the squares of BA , AC : but the square of DC is equal ( 47. 1. ) to the squares of DA , AC , because DAC ...
Seite 41
... square ADEB , and through C draw ( 31. 1 ) CF , parallel to AD or BE ; then AE is equal to the rectangles AF , CE : and AE is the square of AB : and AF is the rectangle contained by BA , AC ; for it is contain- ed by DA , AC , of which ...
... square ADEB , and through C draw ( 31. 1 ) CF , parallel to AD or BE ; then AE is equal to the rectangles AF , CE : and AE is the square of AB : and AF is the rectangle contained by BA , AC ; for it is contain- ed by DA , AC , of which ...
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S 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 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 third triangle ABC triplicate ratio vertex wherefore
Beliebte Passagen
Seite 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 41 - 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.
Seite 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Seite 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Seite 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Seite 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 256 - 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.
Seite 129 - 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.
Seite 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Seite 20 - ANY two angles of a triangle are together less than two right angles.