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 53
... circle , are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line ...
... circle , are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line ...
Seite 54
... circle ABC . Which was to be found . C ། G F B D E COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR ...
... circle ABC . Which was to be found . C ། G F B D E COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR ...
Seite 55
... circle , and join EA , EB . Then , because AF is equal to FB , and FE common to the two triangles AFE , BFE , there ... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ...
... circle , and join EA , EB . Then , because AF is equal to FB , and FE common to the two triangles AFE , BFE , there ... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ...
Seite 56
... a circle , & c . Q. E. D. PROP . V. THEOR . Ir two circles cut one another , they shall not have the same centre . Let the two circles ABC , CDG cut one another in the points B , C ; they have not the same centre . C For , if it be ...
... a circle , & c . Q. E. D. PROP . V. THEOR . Ir two circles cut one another , they shall not have the same centre . Let the two circles ABC , CDG cut one another in the points B , C ; they have not the same centre . C For , if it be ...
Seite 57
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
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.