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 100.
Σελίδα 13
... equal to AD by def " ( Def . 15 ) . But by construction the straight line c is equal to AD ; and things that are ... ABC , DEF be two triangles , which have ( 1 ) the two sides BA , AC of the one re- spectively equal to the two sides ED ...
... equal to AD by def " ( Def . 15 ) . But by construction the straight line c is equal to AD ; and things that are ... ABC , DEF be two triangles , which have ( 1 ) the two sides BA , AC of the one re- spectively equal to the two sides ED ...
Σελίδα 14
Euclides Henry Judge Hose. ABC , DEF , to which the equal sides AC , DF are opposite , shall be equal ; and ACB , DFE , to which the equal sides AB , DE are opposite , shall be equal ; ( 3 ) the triangle ABC shall be equal to the ...
Euclides Henry Judge Hose. ABC , DEF , to which the equal sides AC , DF are opposite , shall be equal ; and ACB , DFE , to which the equal sides AB , DE are opposite , shall be equal ; ( 3 ) the triangle ABC shall be equal to the ...
Σελίδα 16
... ABC is equal ( Ax . 3 ) to the remaining angle ACB . And it was proved above that angle FBC is equal to angle GCB . Therefore ( 1 ) the angles ABC , ACB at the base BC are equal ; ( 2 ) the angles CBD , BCE on the other side of the base BC ...
... ABC is equal ( Ax . 3 ) to the remaining angle ACB . And it was proved above that angle FBC is equal to angle GCB . Therefore ( 1 ) the angles ABC , ACB at the base BC are equal ; ( 2 ) the angles CBD , BCE on the other side of the base BC ...
Σελίδα 17
... equal to the triangle ABC , that is , the part equal to the whole , which is impossible ( Ax . 9 ) . Therefore AB , AC are not unequal , that is , the side AC is equal to the side AB . Which was to be proved . COR . - Every equiangular ...
... equal to the triangle ABC , that is , the part equal to the whole , which is impossible ( Ax . 9 ) . Therefore AB , AC are not unequal , that is , the side AC is equal to the side AB . Which was to be proved . COR . - Every equiangular ...
Σελίδα 19
... equal to BD by hyps : which is impossible . Hence in every case it has been shewn impossible for there to be on the same base AB , and on the same A C D B side of it , two ... ABC shall be equal to I. ] 19 . PROPOSITIONS VII . VIII .
... equal to BD by hyps : which is impossible . Hence in every case it has been shewn impossible for there to be on the same base AB , and on the same A C D B side of it , two ... ABC shall be equal to I. ] 19 . PROPOSITIONS VII . VIII .
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.