The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Βιβλίο 11853 |
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Αποτελέσματα 1 - 5 από τα 90.
Σελίδα 3
... equal to one an- other , each of these angles is defined to be a right angle ; and each of the straight lines is ... thing . XIV . A figure is a portion of space which is enclosed by one or more boundaries ; and when all the points in a ...
... equal to one an- other , each of these angles is defined to be a right angle ; and each of the straight lines is ... thing . XIV . A figure is a portion of space which is enclosed by one or more boundaries ; and when all the points in a ...
Σελίδα 7
... tance from that centre ; or , what is the same thing , with any given point as centre , and with any given finite straight line drawn from that point as radius . AXIOMS . I. Things that are equal to the same 1. ] POSTULATES . Postulates.
... tance from that centre ; or , what is the same thing , with any given point as centre , and with any given finite straight line drawn from that point as radius . AXIOMS . I. Things that are equal to the same 1. ] POSTULATES . Postulates.
Σελίδα 8
Euclides Henry Judge Hose. AXIOMS . I. Things that are equal to the same thing are equal to one another . II . If equals , or the same thing , be added to equals , the sums are equal . III . If equals , or the same thing , be taken from ...
Euclides Henry Judge Hose. AXIOMS . I. Things that are equal to the same thing are equal to one another . II . If equals , or the same thing , be added to equals , the sums are equal . III . If equals , or the same thing , be taken from ...
Σελίδα 11
... equal to BA for the same reason . Hence AG , BG are each of them equal to AB ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) therefore AG is equal to BG , and the three straight lines AB , BG , GA , are ...
... equal to BA for the same reason . Hence AG , BG are each of them equal to AB ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) therefore AG is equal to BG , and the three straight lines AB , BG , GA , are ...
Σελίδα 12
... equals DL , DG , take away the equals DA , DB : then the remainders are equal ( Ax . 3 ) , or AL is equal to BG . But BC also is equal to BG ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) ; therefore AL is ...
... equals DL , DG , take away the equals DA , DB : then the remainders are equal ( Ax . 3 ) , or AL is equal to BG . But BC also is equal to BG ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) ; therefore AL is ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Δημοφιλή αποσπάσματα
Σελίδα 39 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Σελίδα 52 - 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.
Σελίδα 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 5 - 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.
Σελίδα 11 - 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.
Σελίδα 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 66 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Σελίδα 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.