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 sider |
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Side 3
... contained by no more than three plane angles ; for in other cases , two solid figures may be contained by similar planes of the same num- ber and magnitude , and yet be unequal to one another , as shall be made evi- dent in the Notes ...
... contained by no more than three plane angles ; for in other cases , two solid figures may be contained by similar planes of the same num- ber and magnitude , and yet be unequal to one another , as shall be made evi- dent in the Notes ...
Side 4
... contained by no more than three plane angles ; nor of this case is there any Demonstration in the Elements we now have , though it is quite neces- sary there should be one . Now , upon the 10th Definition of this Book depend the 25th ...
... contained by no more than three plane angles ; nor of this case is there any Demonstration in the Elements we now have , though it is quite neces- sary there should be one . Now , upon the 10th Definition of this Book depend the 25th ...
Side 6
... contained by AB , DB , is named the angle ABD , or DBA ; and that which is contained by DB , CB ' is called the angle DBC , or CBD ; but , if there be only one angle ' at a point , it may be expressed by the letter placed at that point ...
... contained by AB , DB , is named the angle ABD , or DBA ; and that which is contained by DB , CB ' is called the angle DBC , or CBD ; but , if there be only one angle ' at a point , it may be expressed by the letter placed at that point ...
Side 7
... contained by a diameter and the part of the circumference cut off by that diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . " XX . Rectilineal figures are those ...
... contained by a diameter and the part of the circumference cut off by that diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . " XX . Rectilineal figures are those ...
Side 12
... contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which was to be demonstrated ...
... contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which was to be demonstrated ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 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.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 20 - ANY two angles of a triangle are together less than two right angles.