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 385
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the 49 PLANE ...
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the 49 PLANE ...
Seite 386
... radius of the first is to the radius of the second . Let AC , MN be measures of the angle ABC , according to def . 1 , CD the sine , DA the versed line , AE the tangent , and BE the secant of the arch AC , according to def . 4 , 5 , 6 ...
... radius of the first is to the radius of the second . Let AC , MN be measures of the angle ABC , according to def . 1 , CD the sine , DA the versed line , AE the tangent , and BE the secant of the arch AC , according to def . 4 , 5 , 6 ...
Seite 387
... radius contains a given number ; and , vice versa , a number expressing the length of the sine , versed sine , tangent , and secant , being given , the angle of which it is the sine , versed sine , tangent , and secant , may be found ...
... radius contains a given number ; and , vice versa , a number expressing the length of the sine , versed sine , tangent , and secant , being given , the angle of which it is the sine , versed sine , tangent , and secant , may be found ...
Seite 388
... radius , the sides are the sines of the an- gles opposite to them , and the radius is the sine of a right angle ( cor . to def . 4. ) which is opposite to the hypothenuse . In any oblique angled triangle ABC , any two sides AB , AC will ...
... radius , the sides are the sines of the an- gles opposite to them , and the radius is the sine of a right angle ( cor . to def . 4. ) which is opposite to the hypothenuse . In any oblique angled triangle ABC , any two sides AB , AC will ...
Seite 389
... radius is to the tangent of an angle ; and the radius is to the tangent of the excess of this angle above half a right angle , as the tangent of half the sum of the angles B and C at the base is to the tangent of half their difference ...
... radius is to the tangent of an angle ; and the radius is to the tangent of the excess of this angle above half a right angle , as the tangent of half the sum of the angles B and C at the base is to the tangent of half their difference ...
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.