Handbuch der Literaturwissenschaft: Die griechische Dichtung

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Monograph

Persistent identifier:: 1916598714

Author:: Harzer, Friedrich

Title:: Die Siegellackfabrikation nach den neuesten Verfahren und den bewährtesten Vorschriften

Scope:: 63 Seiten

Year of publication:: 1848

Place of publication:: Weimar

Identifier (digital):: 1916598714

Reihe:: Neuer Schauplatz der Künste und Handwerke (170)

Signature of the source:: a 3726/1(170)/1848

Language:: German

Publisher of the original:: Verlag und Druck von B. F. Voigt.

Usage licence:: Public Domain Mark 1.0

Printer:: Voigt, Bernhard Friedrich

Publisher of the digital copy:: Technische Informationsbibliothek (TIB)

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2025

Document type:: Monograph

Collection:: Work and administration; Chemistry

COORDINATES [I. 1 0. Prove that the mean point of the vertices of a quadrilateral coincides with the mid-point of the line joining the mid-points of the diagonals. 11. Prove that the medians of a quadrilateral (the lines joining the mid points of opposite sides) bisect one another. 12. Apply Ptolemy’s Theorem (AB. CD-f BC. AD=AC. BD) to prove that the points 1, - 2 ; - 2, - 1 ; 4, 7 ; 6, 3 are concyclic. 13. Apply Ptolemy’s Theorem in the same way to the points — 1, - 5 ; 1, — 1 ; 2, 1 ; 3, 3. Plot the points, and show by applying the test AB+ BC=AC that the four points are collinear. 14. Show that the point 7, 5 has the same position-ratio with respect to the two pairs of points 1, 2 ; 5, 4 and — 5, - 1 ; 3, 3. 15. Find the coordinates of a point which has the same position-ratio with respect to the two pairs of collinear points -4, 11 ; 16, -4 and — 16, 20 ; 24, - 10. 1 6. Show that there are two points whose position-ratios with respect to the two pairs of points — 9, — 2 ; — 3, 1 and —1,2; 5, 5 are equal, but of opposite sign. 17. Given two pairs of points A, B and C, D in a line, show that there are two points (real, coincident, or imaginary) whose position-ratios with respect to A, B and C, D have a given ratio. Explain the apparent abnormality when this ratio = 1.

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