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 |
Inni boken
Resultat 1-5 av 100
Side 10
... draw the straight lines ( 2. Post . ) CA , CB to the points A , B ; ABC shall be an equilateral triangle . A B E ... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is ...
... draw the straight lines ( 2. Post . ) CA , CB to the points A , B ; ABC shall be an equilateral triangle . A B E ... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is ...
Side 11
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB .. FROM the greater of two ... draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the dis- tance AD , describe ( 3. Post ...
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB .. FROM the greater of two ... 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 16
... draw a straight line from the point C at right angles to AB . * Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle , DFE , and join FC ; the straight line FC drawn from ...
... draw a straight line from the point C at right angles to AB . * Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle , DFE , and join FC ; the straight line FC drawn from ...
Side 17
... drawn from the given point C , is per- pendicular to the given straight line AB . A F C H G B D Because FH is equal to HG , and HC , common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to ...
... drawn from the given point C , is per- pendicular to the given straight line AB . A F C H G B D Because FH is equal to HG , and HC , common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to ...
Side 21
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
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.