The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 sider |
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Side 15
... base BC coincide with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that ...
... base BC coincide with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that ...
Side 17
... base DF is equal to the base 录 EF ; therefore the angle DCF is equal to the angle * 8. 1 . ECF ; and they are adjacent angles . But , when the adjacent angles which one straight line makes with another straight line are equal to one ...
... base DF is equal to the base 录 EF ; therefore the angle DCF is equal to the angle * 8. 1 . ECF ; and they are adjacent angles . But , when the adjacent angles which one straight line makes with another straight line are equal to one ...
Side 18
... base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of ...
... base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of ...
Side 21
... base AB is equal to the base CF , * 4. 1 . and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
... base AB is equal to the base CF , * 4. 1 . and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
Side 26
... base FG to the base DE ; therefore the angle FAG is equal to the angle DCE . Wherefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP ...
... base FG to the base DE ; therefore the angle FAG is equal to the angle DCE . Wherefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1838 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2023 |
Vanlige uttrykk og setninger
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Populære avsnitt
Side 173 - 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 56 - Iff 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 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Side 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 23 - Any two sides of a triangle are together greater than the third side.
Side 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Side 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Side 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.