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 11
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . C D B A F From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the dis- tance AD , describe ( 3. Post ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . C D B A F From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the dis- tance AD , describe ( 3. Post ...
Side 13
... greater than the other ; let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the 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 ...
... greater than the other ; let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the 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 ...
Side 14
... greater than the angle BCD ; therefore the angle ADC is great- er also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but ...
... greater than the angle BCD ; therefore the angle ADC is great- er also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but ...
Side 19
... greater than either of the interior opposite angles , CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ... greater than the an- gle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be ...
... greater than either of the interior opposite angles , CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ... greater than the an- gle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be ...
Side 20
... greater than the angles ABC , B D ACB ; but ACD , ACB are together equal ( 13.1 . ) to two right angles ; therefore ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
... greater than the angles ABC , B D ACB ; but ACD , ACB are together equal ( 13.1 . ) to two right angles ; therefore ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
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.