The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Seite 13
... sides AC , AF , and BC , BF . A more general proposition than the following will be seen under Prop . III . See also Prop . XXII . C E This Problem is practically applied in Fortification . C B PROP . A. PROB . GEN . ENUN . - 13.
... sides AC , AF , and BC , BF . A more general proposition than the following will be seen under Prop . III . See also Prop . XXII . C E This Problem is practically applied in Fortification . C B PROP . A. PROB . GEN . ENUN . - 13.
Seite 14
... ENUN . From a given point to draw a straight line equal to a given straight line . PART ENUN . - Let A be the gn . pt . , BC the gn . st . line ; then it is required to draw from the pt . A , a st . line = BC . CONST .-- From the pt . A ...
... ENUN . From a given point to draw a straight line equal to a given straight line . PART ENUN . - Let A be the gn . pt . , BC the gn . st . line ; then it is required to draw from the pt . A , a st . line = BC . CONST .-- From the pt . A ...
Seite 16
... ENUN . - From the greater of two given straight lines to cut off a part equal to the less . PART . ENUN . - Let AB and c be the two gn . st . lines , of which AB is > c ; then it is required to cut off from AB a part = C. A D E B F ...
... ENUN . - From the greater of two given straight lines to cut off a part equal to the less . PART . ENUN . - Let AB and c be the two gn . st . lines , of which AB is > c ; then it is required to cut off from AB a part = C. A D E B F ...
Seite 17
... ENUN . - To describe an isosceles △ on a given finite straight line . PART . ENUN . - Let AB be the gn . st . line ; then it is required to describe an isosc . A upon it . CONST . - In AB , produced if neces- sary , take any pt . D ...
... ENUN . - To describe an isosceles △ on a given finite straight line . PART . ENUN . - Let AB be the gn . st . line ; then it is required to describe an isosc . A upon it . CONST . - In AB , produced if neces- sary , take any pt . D ...
Seite 18
... ENUN . - Let ABC , DEF , be two As , which have the two sides AB , AC to the two sides DE , DF , each to each ; viz . AB DF , and B BAC = EDF ; = DE , and AC = also the then the base BC shall = base EF ; and the area of the Δ ABC shall ...
... ENUN . - Let ABC , DEF , be two As , which have the two sides AB , AC to the two sides DE , DF , each to each ; viz . AB DF , and B BAC = EDF ; = DE , and AC = also the then the base BC shall = base EF ; and the area of the Δ ABC shall ...
Häufige Begriffe und Wortgruppen
ABCD adjacent angle contained base BC bisect CD Prop coincide Const CONST.-In CONST.-Join CONST.-Let DEMONST.-Because DEMONST.-For demonstration diam diameter draw EBCF ENUN ENUN.-If ENUN.-Let ABC ENUN.-To ENUN.-To describe equal sides equilateral Euclid EUCLID'S ELEMENTS exterior four rt given point given straight line interior and opposite interior opposite isosceles join Let ABC line be drawn line drawn meet opposite angles opposite sides parallel parallelogram perpendicular Post PROB produced Proposition proved rectilineal figure rhombus right angles side BC square take any pt THEOR THEOR.-If Theorem trapezium trapezium ABCD vertical Wherefore XXIX XXXI XXXII XXXIV XXXVIII
Beliebte Passagen
Seite 58 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 24 - Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity, equal to one another.
Seite 34 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Seite 6 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Seite 109 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Seite 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Seite 99 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 49 - If, from the ends of the side of a triangle, there be 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...
Seite 104 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Seite 6 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.