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 σελίδες |
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Σελίδα 40
... contained by any two of the straight lines which contain one of the right angles . II . E D In every parallelogram ... rectangle contained by the two straight lines , is equal to the rectangles contained by the un- divided line , and the ...
... contained by any two of the straight lines which contain one of the right angles . II . E D In every parallelogram ... rectangle contained by the two straight lines , is equal to the rectangles contained by the un- divided line , and the ...
Σελίδα 41
... rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c . Q. E. D. ...
... rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c . Q. E. D. ...
Σελίδα 42
... rectangle AB , BC , is equal to the rectangle AC , CB , to- gether with the square of BC . If therefore a straight line , & c . Q. E. D. PROP . IV . THEOR . Ir a ... rectangle contained by the unequal 42 BOOK II . THE ELEMENTS OF EUCLID .
... rectangle AB , BC , is equal to the rectangle AC , CB , to- gether with the square of BC . If therefore a straight line , & c . Q. E. D. PROP . IV . THEOR . Ir a ... rectangle contained by the unequal 42 BOOK II . THE ELEMENTS OF EUCLID .
Σελίδα 43
... rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half the line . Let the straight line AB be divided into two equal parts in the point C , and into ...
... rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half the line . Let the straight line AB be divided into two equal parts in the point C , and into ...
Σελίδα 44
... rectangle contained by AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is equal to the rectangle AD , DB , add to each of these LG , which is equal to the square of CB , therefore the rectangle AD , DB ...
... rectangle contained by AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is equal to the rectangle AD , DB , add to each of these LG , which is equal to the square of CB , therefore the rectangle AD , DB ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Σελίδα 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.
Σελίδα 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 20 - ANY two angles of a triangle are together less than two right angles.